(V(8275, 1, 12447) - 1)/(V(8275, 1, 27) - 1)

This prime's information:

Archival tags:

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Lehmer primitive part (archivable *)

Prime on list: yes, rank 4
Subcategory: "Lehmer primitive part"
(archival tag id 239477, tag last modified 2025-09-17 05:37:12)

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Serge Batalov writes (22 Aug 2025):  (report abuse)

This Lehmer primitive part is proven using CHG with N-1 factored to 26.30% and helper prime factors (p6338, p2057) proven with CM, and a c139 factored with msieve. Report is available. Here is a partial CHG(server) script log: Target "LehmPrim48k" has 48659 digits. Modulus provides 26.303694833878762252%. Right endpoint has 10262 digits. LLL[1, 1] for client 1 has [h, u] = [4, 1] and digits in [1, 123] LLL[2, 1] for client 2 has [h, u] = [4, 1] and digits in [123, 505] LLL[3, 1] for client 3 has [h, u] = [5, 1] and digits in [505, 1786] LLL[4, 1] for client 4 has [h, u] = [5, 1] and digits in [1786, 2427] ... LLL[65, 1] for client 65 has [h, u] = [20, 9] and digits in [10059, 10131] LLL[66, 1] for client 66 has [h, u] = [20, 9] and digits in [10131, 10198] LLL[67, 1] for client 67 has [h, u] = [20, 9] and digits in [10198, 10262] LLL was split between 67 clients. 67 LLL reductions completed in 66.78416666666666667 CPUhours. ... Please wait, while the certificate is saved... A certificate was saved in file "LehmPrim48k_cert.gp". ... Pol[64, 1] with [h, u]=[20, 9] has ratio=0.003728049659738002987 at X, ratio=8.415378897751522524 E-680 at Y, witness=23. Pol[65, 1] with [h, u]=[20, 9] has ratio=0.023357953762571045185 at X, ratio=5.016146682227363578 E-644 at Y, witness=107. Pol[66, 1] with [h, u]=[20, 9] has ratio=7.551660935221329819 E-14 at X, ratio=1.1499241782008381701 E-620 at Y, witness=101. Pol[67, 1] with [h, u]=[20, 9] has ratio=1.4976265353636799078 E-97 at X, ratio=1.4202707053422817058 E-608 at Y, witness=47. Validated in 37 sec.

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.