Pith Number

pith:JNKPIIPA

pith:2026:JNKPIIPAEI6QCDGYOUKH7II23B

not attested not anchored not stored refs resolved

When Does the Dice Sum Become Prime?

Christoph Koutschan, Thotsaporn Aek Thanatipanonda, Tipaluck Krityakierne

Dynamic programming computes the expected number of die rolls until the sum is prime to more than 1000 decimal places.

arxiv:2605.13666 v1 · 2026-05-13 · math.PR · math.CO · math.NT

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\pithnumber{JNKPIIPAEI6QCDGYOUKH7II23B}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

our calculations yield significantly sharper estimates for this expectation and its higher moments than the original results of Conroy, Alon, and Malinovsky. In particular, we determine the expectation to more than 1000 decimal places.

C2weakest assumption

the density of primes implies that the associated survival probability decays exponentially fast, which enables highly accurate truncation estimates.

C3one line summary

The expected number of die rolls until the sum is prime is computed to more than 1000 decimal places via DP truncation with exponential-decay error bounds.

References

9 extracted · 9 resolved · 1 Pith anchors

[1] Noga Alon and Yaakov Malinovsky,Hitting a prime in 2.43 dice rolls (on average), The American Statistician77(3), 301–303, 2023 2023

[2] Noga Alon, Yaakov Malinovsky, Lucy Martinez, and Doron Zeilberger,Hitting k primes by dice rolls, Electronic Journal of Combinatorics32(4), 4.16, 2025 2025

[3] A more recent version (2026) is available athttps://www.madandmoonly.com/ doctormatt/mathematics/dice1.pdf 2018

[4] Lucy Martinez and Doron Zeilberger,How many Dice Rolls Would It Take to Reach Your Favorite Kind of Number?, Maple Transactions3(3), Autumn 2023 2023

[5] Barkley Rosser and Lowell Schoenfeld,Approximate Formulas for some Functions of Prime Numbers, Illinois Journal of Mathematics6(1), 64–94, March 1962 1962

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:17.246519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b54f421e0223d010cd875147fa11ad840c2157528815ca074f1317d9f0288bf

Aliases

arxiv: 2605.13666 · arxiv_version: 2605.13666v1 · doi: 10.48550/arxiv.2605.13666 · pith_short_12: JNKPIIPAEI6Q · pith_short_16: JNKPIIPAEI6QCDGY · pith_short_8: JNKPIIPA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JNKPIIPAEI6QCDGYOUKH7II23B \
  | 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: 4b54f421e0223d010cd875147fa11ad840c2157528815ca074f1317d9f0288bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdbe7cba193d24f1236e8c1d2dea033351e2003a2de02a4e78cd173a59fc32a1",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-13T15:24:36Z",
    "title_canon_sha256": "87e2d8d0c443ad07010a1071b346d338b9cd03772d30af2e394580d73c2477a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13666",
    "kind": "arxiv",
    "version": 1
  }
}