Pith Number

pith:27TEJSGP

pith:2026:27TEJSGPNUWF32HERWE6OSA4IQ

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Simple groups with narrow prime spectrum: Extended list

Andrei V. Zavarnitsine

All non-abelian finite simple groups whose order has largest prime divisor at most 10000 have been determined.

arxiv:2605.16450 v1 · 2026-05-15 · math.GR

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Claims

C1strongest claim

We determine all non-abelian finite simple groups whose order has largest prime divisor not exceeding 10^4.

C2weakest assumption

The classification of finite simple groups is complete and the orders of all known simple groups are correctly tabulated in the literature or databases used by the program.

C3one line summary

All non-abelian finite simple groups with largest prime divisor at most 10^4 are listed via exhaustive computational search over the known simple groups.

References

5 extracted · 5 resolved · 0 Pith anchors

[1] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wil- son, Atlas of finite groups: maximal subgroups and ordinary characters for simple groups. Oxford. Clarendon Press (1985), xxxiii + 25 1985

[2] URL: http://www.gap-system.org 2025

[3] V. D. Mazurov, On the set of orders of elements of a finite group, Algebra and Logic,33, N 1 (1994), 49–55 1994

[4] A. V. Zavarnitsine, Finite simple groups with narrow prime spectrum,Sib. Elect. Math. Reports,6(2009), 1–12. URL: http://semr.math.nsc.ru/v6/p1-12.pdf 2009

[5] A. V. Zavarnitsine, GAP code accompanying this paper (2026). URL:https://github.com/zavandr/pi-simple The tables T able 1: Primes p∈ { 1000, . . . ,10000} with generic Sp 1009, 1013, 1019, 1033, 1039, 2026

Formal links

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Receipt and verification

First computed	2026-05-20T00:02:22.696983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7e644c8cf6d2c5de8e48d89e7481c4425dff74300d75cfdeaf38a6ca3cff177

Aliases

arxiv: 2605.16450 · arxiv_version: 2605.16450v1 · doi: 10.48550/arxiv.2605.16450 · pith_short_12: 27TEJSGPNUWF · pith_short_16: 27TEJSGPNUWF32HE · pith_short_8: 27TEJSGP

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/27TEJSGPNUWF32HERWE6OSA4IQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d7e644c8cf6d2c5de8e48d89e7481c4425dff74300d75cfdeaf38a6ca3cff177

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "b016bc5b3fcbff4a657e38fb11afddc3c94b9c25dd682bab17a397a8e5c46253",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-15T03:18:13Z",
    "title_canon_sha256": "9f3b267e7567b9e94cd517aed1296d660b124d493637355aa448e9c7051d3443"
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  "source": {
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}