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Paper Citation Record · LEDGER

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts

As of 16 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 0 inbound Pith citation observations for arXiv:1908.06964.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.06964 v1

Coverage vector

measured 60 of 60 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T12:24:27.643404Z

measured 60 of 60 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

60 of 60 outbound references displayed

  • verified exact1
  • verified fuzzy54
  • unresolved4
  • parse uncertain0
  • malformed identifier1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4cf26c10-4fab-426a-95ba-9498a24747dd · outbound

This paper cites Mathematics research page,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Mathematics research page,

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation f66d48c7-a872-4ee5-a049-322a60888208 · outbound

This paper cites Prime and prejudice: Primality testing under adversarial conditions,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Prime and prejudice: Primality testing under adversarial conditions,

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.648781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation af9aafe6-424f-485f-baad-3e037741bcd4 · outbound

This paper cites Euler’s criterion,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Euler’s criterion,

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.632100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 834103c8-2cd2-4759-bd1b-f75ca701c145 · outbound

This paper cites an unresolved cited work.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:24:28.616417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.362214Z digest=sha256:d659842721991ad4156d674e03b62533c4dead25871a307339b8bc4a317707f8

Observation eec6f494-97a0-40e6-beae-10d4af2fd496 · outbound

This paper cites Shoup,A computational introduction to number theory and algebra.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Shoup,A computational introduction to number theory and algebra

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.599033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.367354Z digest=sha256:d71d42163810beb7daa89b194a4a13284989dae65f66cb1e2df7cd5bf136e1d1

Observation 81886281-6ccc-4540-9d39-01a3339492ba · outbound

This paper cites Crandall and C.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Crandall and C

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.583401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.372181Z digest=sha256:7f170076efbd098bd3bc695e76c8bf215cd12b377091a4d37a46c6fd74c431ed

Observation 31b4a70e-654e-4e69-859a-c0ce1e89d2ef · outbound

This paper cites Jacobi Symbol,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Jacobi Symbol,

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.567625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.377385Z digest=sha256:9985a207b71b6e801ea517bb567e90bb1a83115c45f897c3f45ab0c12ebc3536

Observation ca789260-ba75-4f98-9407-fcf4ad76a50f · outbound

This paper cites Jacobi Symbol,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Jacobi Symbol,

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.551091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.381905Z digest=sha256:a594fec05848f7f834c096b0a9303ee114c2a550db71571a154427b313387ac0

Observation b1acdbea-c6cd-4d68-be09-8217abd5331d · outbound

This paper cites Maplesoft,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Maplesoft,

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.535913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.386728Z digest=sha256:b5c5655252ab108e169e7aa509775602349a8da07447611588010e3f3ef90840

Observation 848d6f47-f026-42c3-9cbf-39fdafec45aa · outbound

This paper cites PRIMES is in P,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts PRIMES is in P,

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.519903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 4a08103d-1355-43d5-96f3-716c49f3adcc · outbound

This paper cites an unresolved cited work.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:24:28.504717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.395967Z digest=sha256:f85b10f936de7cf2956344d0771a9d335779cb0987c1f6ebec6c357cfff06123

Observation afb0ea61-378f-4779-9f09-78e7cb0bfb6a · outbound

This paper cites The distribution of quadratic and higher residues,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The distribution of quadratic and higher residues,

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.489047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.401037Z digest=sha256:f42b785489ac4abb32b1eead8a1523637a5c8b54b8452d91fd8a929f9c117d3f

Observation 980b3a6c-3f0a-4b87-aecf-c1b4a98a0a7d · outbound

This paper cites The least quadratic non residue,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The least quadratic non residue,

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.473711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.406938Z digest=sha256:ed22819c9b989eda748602852a819e6b36064a4f57334bbaed452fb5b2ecaf7c

Observation f545b8e4-4535-44a0-b99a-3d44ba678425 · outbound

This paper cites The distribution of quadratic residues and non-residues,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The distribution of quadratic residues and non-residues,

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.458119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.411761Z digest=sha256:e23652cf9e51034c24c58e7bdd3bc7445a8f95f30f3c74994600574877c24698

Observation e2d7b16a-1b68-4391-aaa4-5a46aa967917 · outbound

This paper cites Lower bounds for least quadratic non-residues,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Lower bounds for least quadratic non-residues,

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.442823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.416426Z digest=sha256:df9e784051e29e3cf644a38e65b064ea59a7aa920adbe5290f001bfb4fb87667

Observation b7ac022a-ff90-426b-a167-93a6d03d9551 · outbound

This paper cites Constructing nonresidues in finite fields and the Extended Riemann Hypothesis,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Constructing nonresidues in finite fields and the Extended Riemann Hypothesis,

Reference 16

Resolution
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raw_fallback, observed 2026-08-14T12:24:28.427550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.421106Z digest=sha256:4d35aa61c45542de960ebf00f305cc1e7a050e091966c2967fa9f41d3d6a24a1

Observation c193fe4a-bff4-4a37-ac61-d6ccd680aaf1 · outbound

This paper cites On the distribution of quadratic residues and nonresidues modulo a prime number,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On the distribution of quadratic residues and nonresidues modulo a prime number,

Reference 17

Resolution
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raw_fallback, observed 2026-08-14T12:24:28.411064Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.425748Z digest=sha256:7e368b837e2ba55545c82f464fb7c7ea7accfc47e3a9beecaa141561aaf816a7

Observation e7c72aea-e80a-4966-af97-c7b356cc0251 · outbound

This paper cites Quadratic nonresidues and applications,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Quadratic nonresidues and applications,

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.394634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.430463Z digest=sha256:d411bb8a07c853324b73ddf2c3cb4c48c9582c3394c6f21beb91a06ed5fbbee8

Observation a0ae319e-7524-4b69-833f-762dfca10df4 · outbound

This paper cites Complexity of Computing Quadratic Nonresidues.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Complexity of Computing Quadratic Nonresidues

Reference 19

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation bdea8dd6-ea53-46b4-863a-f61d9c822888 · outbound

This paper cites On taking square roots and constructing quadratic nonresidues over finite fields,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On taking square roots and constructing quadratic nonresidues over finite fields,

Reference 20

Resolution
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raw_fallback, observed 2026-08-14T12:24:28.379363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 56dbab5d-3824-4551-b3bd-f80b9deb51cd · outbound

This paper cites The least quadratic nonresidue, and the square root barrier,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The least quadratic nonresidue, and the square root barrier,

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.363297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation d37623a2-f276-4afe-9bb4-751085e3fe47 · outbound

This paper cites On taking square roots without quadratic nonresidues over finite fields,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On taking square roots without quadratic nonresidues over finite fields,

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.347381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 26843eca-152c-4caf-bdaf-5943fa5a44ef · outbound

This paper cites Conditional bounds for the least quadratic non- residue and related problems,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Conditional bounds for the least quadratic non- residue and related problems,

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.329279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.458308Z digest=sha256:504ce1291a24b4524955d0ebac3de0611910588803a7f14af7a512d2efa692a6

Observation 604f9364-9385-4d8f-be50-804c48074b15 · outbound

This paper cites The elliott–halberstam conjecture implies the vinogradov least quadratic nonresidue conjecture,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The elliott–halberstam conjecture implies the vinogradov least quadratic nonresidue conjecture,

Reference 24

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verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.312222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.462972Z digest=sha256:b804ec6ba5ea55255b514f0b0a1dc23a70464a1f6e3e3e0976a5c987fb07e81e

Observation c39d9251-f33e-44df-88e6-49a2356a4c38 · outbound

This paper cites PRIMES is in P.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts PRIMES is in P

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.296505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.467826Z digest=sha256:a6e0e469c1da4749f6c6c42e29deda654dbb8b3e218100ce92951e1d8858ea55

Observation abfea5bf-f2e6-4c96-a79c-3aa1c42a4878 · outbound

This paper cites Primality testing with gaussian periods,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Primality testing with gaussian periods,

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.280336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.472567Z digest=sha256:803b20026b2da6202f5adc283a8fecf4e60bc41f2072fb21f48bbb08e3765e29

Observation d90cf7dc-700d-4315-a10d-f71468003d41 · outbound

This paper cites Primality testing with gaussian periods,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Primality testing with gaussian periods,

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.262970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.477226Z digest=sha256:afbba7a15db68f6eac63a94f6e48cb340cf4964ffda9cf1796ff5458a9107613

Observation 551c3434-ae76-45fd-ad72-670286ea1ef6 · outbound

This paper cites Proving primality in essentially quartic random time,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Proving primality in essentially quartic random time,

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.247058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.482455Z digest=sha256:1e2c3f8afa002ad61f488d3971548335ea6e96ce3b2ac0f7b0c2cd9d586d5b3d

Observation 32f114a2-4834-42c9-bcd8-2ca08ec1e4a3 · outbound

This paper cites On the complexity of multiplication in finite fields,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On the complexity of multiplication in finite fields,

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.231044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.487109Z digest=sha256:fa89f7c297fd78794bc34cd80fa6ab14918a3e9686259192921327148becfb74

Observation ec38d332-e870-4ba6-9f19-299a2c4b2e33 · outbound

This paper cites Hensel lifting and polynomial division,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Hensel lifting and polynomial division,

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.213188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.491826Z digest=sha256:5acc7ac9021fcf56a1484b9e911fc2058a1c18b0f970decbaa8560ef3708ea08

Observation 90a205b9-38f2-4c84-8479-dbdca198a901 · outbound

This paper cites Sparse polynomial multiplication and division in maple 14,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Sparse polynomial multiplication and division in maple 14,

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.197428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.496489Z digest=sha256:06cfe8b29d64775f9ccb7112b5774bf501f0977e24e4022bbdef108336990ed6

Observation 5c88916b-b890-4b99-926b-6a4ebdfaa6f7 · outbound

This paper cites On newton–raphson iteration for multiplicative inverses modulo prime powers,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On newton–raphson iteration for multiplicative inverses modulo prime powers,

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.180054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.501124Z digest=sha256:51351e4fd6bd35a6877e6e429d27f4e61b675fd7fd5099625d0ff8ee2ad99560

Observation 8f37a351-3e1d-430f-997f-6e524f92d909 · outbound

This paper cites Faster polynomial multiplication over finite fields using cyclotomic coefficient rings,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Faster polynomial multiplication over finite fields using cyclotomic coefficient rings,

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.164273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.505755Z digest=sha256:68d1490f8bd2ffecbc797b54a72fce679ce52a032e24f0d5427bd1276b978659

Observation 795e2cdd-71dd-45eb-be9a-d6932339b0e2 · outbound

This paper cites Carmichael numbers,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Carmichael numbers,

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.146094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.510136Z digest=sha256:c2dd751fcd17f649df426d22c3d32c0b0ae02fa44fdd9f05c1608334f48fd475

Observation 22bfd9d0-80ed-4e66-8691-d77ed234f32f · outbound

This paper cites Strong pseudoprime,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Strong pseudoprime,

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.129933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.514925Z digest=sha256:acd4e91ead683424c449de24761c823fbf31a880e1029c9e9fa8285f5aacee3b

Observation 290dd393-832a-4699-93e5-bfddc3ebb664 · outbound

This paper cites Miller–Rabin primality test,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Miller–Rabin primality test,

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.113318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.520009Z digest=sha256:03ade864f76cdfbd4fde137a763e8f33b8a432c0ba1b3ea142b4e1952375e90c

Observation b3490ed3-1949-4ec9-bbeb-42cd0f2561ee · outbound

This paper cites an unresolved cited work.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Unresolved cited work

Reference 37

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:24:28.096647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.524734Z digest=sha256:4cc5266ae7af2685dbfaca5db77387e6f4c83592ee763f0a5ee43ae6464b8499

Observation 69af1a07-bcb5-4213-931e-4d55b265a9f9 · outbound

This paper cites Cyclotomic polynomial,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Cyclotomic polynomial,

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.080218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.529170Z digest=sha256:6a87872fd2ba2e7411b602809784a2fe04dffbb7b2416cb2966e3e4875dba43a

Observation 384ad439-a7b0-4435-879d-f9e0dede56bb · outbound

This paper cites Primorial,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Primorial,

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.063636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.533697Z digest=sha256:019d2bc2a666e5060e9e072cd659fc0569d7fa0883f25c7253a33686153daba5

Observation 6285a33a-a92a-4192-a1e7-7ca400bc64cc · outbound

This paper cites Parhami, Computer Arithmetic Algorithms and Hardware Designs.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Parhami, Computer Arithmetic Algorithms and Hardware Designs

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.046987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.538398Z digest=sha256:295c99015705118ef3b617285c64141cd4f0867478c95005f076cd6e18df3d17

Observation 922e8011-0007-4659-9d18-6142d1f12473 · outbound

This paper cites New distributed algorithms for fast sign detection in residue number systems (rns),.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts New distributed algorithms for fast sign detection in residue number systems (rns),

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.029959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.543052Z digest=sha256:1771ed4ca74c9ac97c67cc28cdb14894f964a77783b277f6f0f449a6bc19bc61

Observation 078db4a6-bcf3-49f4-8a36-07867e5217c8 · outbound

This paper cites Bertrand’s postulate,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Bertrand’s postulate,

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:28.012767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.547982Z digest=sha256:6c1177a7c50af2c18c4bc80b5df6b7a7bfefe3f9256c10bc067d1267b54d0756

Observation 12d5ec5d-e83f-4c19-8fdf-3b551cb9388b · outbound

This paper cites Prime–counting function,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Prime–counting function,

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.995506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.552629Z digest=sha256:721154aebbaa36c63abbf308917ad77b9cf076ea89ceae37cb3a93464c32cab7

Observation 52a0117b-5041-431d-82bd-0288c6063686 · outbound

This paper cites Baillie–PSW primality test,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Baillie–PSW primality test,

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.979490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.557612Z digest=sha256:affc1bda1d301ee6ae72b558501559a79b4e8595ac6120ee7371f8c35187da92

Observation 2e77c9df-1819-4170-961b-aade6b0049cc · outbound

This paper cites Quadratic residue,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Quadratic residue,

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.962882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.562308Z digest=sha256:b217ed307f3148258d933a260b4bc26cd2f0c47d453d06c53add36cef3a6df72

Observation 71842e25-8e26-44c2-9c08-d1a1cf1bfb56 · outbound

This paper cites Carmichael numbers in number rings,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Carmichael numbers in number rings,

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.947120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.566992Z digest=sha256:4a059df283820748d00146be00a177d32f6c591b0aed7127d6c9e0e13c106e9f

Observation fb68eaf1-1c9b-48d1-bdbf-8d6a3d234f13 · outbound

This paper cites Constructing carmichael numbers which are strong pseudoprimes to several bases,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Constructing carmichael numbers which are strong pseudoprimes to several bases,

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.931825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.571955Z digest=sha256:3c3c62c8ba125372875534cf464a7dc3aa5509634c3b1a2ac4c6a4619a5fee7b

Observation 31df7f33-a9d5-4a0e-a940-96a00b1561b9 · outbound

This paper cites The carmichael numbers up to 1021,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The carmichael numbers up to 1021,

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.915383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.576724Z digest=sha256:2ca56f5265bd4dcbf3f3c136d2695aa9f802317d0e140078e71564c20f6e497c

Observation afd3e5a0-e9c4-4f45-953f-77a3d7b7191e · outbound

This paper cites PRP Records, Probable Primes Top 10000 ,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts PRP Records, Probable Primes Top 10000 ,

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.898589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.581806Z digest=sha256:80c304eecdeac1135b6a5b25fd47e93d35d4739cdb04b6f8782b2ffbfad93150

Observation a667b6bf-b1ce-4e39-b960-2738060aa37e · outbound

This paper cites A014233 : Smallest odd number for which Miller-Rabin primality test on bases≤n-th prime does not reveal compositeness.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts A014233 : Smallest odd number for which Miller-Rabin primality test on bases≤n-th prime does not reveal compositeness

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.882405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.586693Z digest=sha256:73d1116737fc736f7c155e9c03093c0e4677f9f883243a850aeec3119520d9fc

Observation f99c5b10-bb50-4290-8948-217ab5f794e0 · outbound

This paper cites A001262 : Strong pseudoprimes to base 2,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts A001262 : Strong pseudoprimes to base 2,

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.865133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.591331Z digest=sha256:2a5f86072ab2cc5c2a38326740f005b622afca679e044ee01b72f766d7511d5d

Observation eea7f230-e2dd-4f73-bb90-28bd8176dfd2 · outbound

This paper cites Higher-order Carmichael numbers,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Higher-order Carmichael numbers,

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.849285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.596238Z digest=sha256:841b9bbc9de936246c29240ff463f5d1cb1510eebc395a7e36aec48951b2c8c1

Observation 73789536-1f43-4995-a25e-c96181a73cab · outbound

This paper cites Higher-order carmichael numbers,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Higher-order carmichael numbers,

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.833362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.601266Z digest=sha256:1a88689b6403ff3557faf22acc7aed463b48e06a2c442fa3c10d70fd92dba9aa

Observation 6b55cf2a-c6ef-42c6-ab6d-c8be1cba331b · outbound

This paper cites Pepin’s Test,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Pepin’s Test,

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.817217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.606467Z digest=sha256:5612c78d8dc3c3ad94af9d09cd421f42a456af5ae6546583ba12fb68e5655ceb

Observation b72f67b5-c881-437f-a718-52ae800ddd6d · outbound

This paper cites Fermat number,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Fermat number,

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.801099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.611151Z digest=sha256:6ce7e2c01199d9a580ecc98f96daf3a684300fd373f77f972ac5434c63c3f979

Observation df189629-dd93-4830-b7be-97e84c6bece2 · outbound

This paper cites Mersenne prime,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Mersenne prime,

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.783222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.615777Z digest=sha256:8d59696613b34fa76fd88ff82b29a9a9b5dfa0cbe2ecbc029509e198dbad5066

Observation a1d86ce6-315c-49a4-83ce-83f7236cd096 · outbound

This paper cites Lucas–Lehmer primality test,.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Lucas–Lehmer primality test,

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.766025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.620221Z digest=sha256:da339e7f6cb5b916892e61c15297a95088d5882e2ae11e6716645f740e2ec983

Observation 8b7ac6e2-053b-4562-bfba-eaf8b88d1534 · outbound

This paper cites an unresolved cited work.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:24:27.746314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.627508Z digest=sha256:68785b8a24d39ece14c28cb67ec4c9568f8ac9cf20d92153eb0433d7ef7b070b

Observation fbba230a-d446-4f6f-90a7-34bdee89472f · outbound

This paper cites probable prime.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts probable prime

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.728469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.632303Z digest=sha256:4f151473e0ba65e2002f04c8156b8c935c32493ae1236c9ec9186c46f3b2a9ce

Observation 33321de1-54ea-4f23-8207-82a4ba37dbc1 · outbound

This paper cites conjugate.

PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts conjugate

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:24:27.709237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:24:27.643404Z digest=sha256:4ee1b526dbc41cf186299a2c9a5a5b39fdc2b7a7cb25410e248ae24a92164834

Pith citing papers

No inbound Pith citation observations are available.