(V(10981, 1, 17553) + 1)/(V(10981, 1, 3) + 1)

This prime's information:

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.

Cyclotomy Proof (tolerated *)

Prime on list: no, rank 1
Subcategory: "Cyclotomy Proof"
(archival tag id 239488, tag last modified 2025-08-29 21:37:20)

Lehmer primitive part (archivable *)

Prime on list: yes, rank 2
Subcategory: "Lehmer primitive part"
(archival tag id 239489, tag last modified 2025-09-01 22:37:12)

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Serge Batalov writes (29 Aug 2025):  (report abuse)

This Lehmer primitive part is proven using CHG with N-1 factored to 26.13% and helper prime factors (p8678, p1733) proven with CM, and a c146 factored with msieve. Ryan Propper provided important boost to the factorization of N-1 from 25.2% to 26.13% (including a remarkable factor p67 for a c423 = one of the algebraic halves of primU(10981,1,399)). Report is available. Here is a partial CHG(server) script log: Target "LehmPrim70k" has 70914 digits. Modulus provides 26.148575514581741922%. Right endpoint has 15286 digits. LLL[1, 1] for client 1 has [h, u] = [4, 1] and digits in [1, 477] LLL[2, 1] for client 2 has [h, u] = [5, 1] and digits in [477, 2419] LLL[3, 1] for client 3 has [h, u] = [5, 1] and digits in [2419, 3389] LLL[4, 1] for client 4 has [h, u] = [7, 2] and digits in [3389, 4491] ... LLL[69, 1] for client 69 has [h, u] = [23, 10] and digits in [15022, 15098] LLL[70, 1] for client 70 has [h, u] = [23, 10] and digits in [15098, 15166] LLL[71, 1] for client 71 has [h, u] = [24, 11] and digits in [15166, 15286] LLL was split between 71 clients. 71 LLL reductions completed in ~100 CPUhours. ... Please wait, while the certificate is saved... A certificate was saved in file "LehmPrim70k_cert.gp". ... Pol[67, 1] with [h, u]=[23, 10] has ratio=0.004636393675005166994 at X, ratio=7.403094084317438998 E-914 at Y, witness=31. Pol[68, 1] with [h, u]=[23, 10] has ratio=0.007437174580983283418 at X, ratio=5.215794765920094433 E-831 at Y, witness=53. Pol[69, 1] with [h, u]=[23, 10] has ratio=0.005273975923880440106 at X, ratio=1.1504916805761874578 E-755 at Y, witness=79. Pol[70, 1] with [h, u]=[23, 10] has ratio=0.004288398549295792086 at X, ratio=3.379114481383864073 E-687 at Y, witness=29. Pol[71, 1] with [h, u]=[24, 11] has ratio=0.006101867006692129430 at X, ratio=9.039889030216546318 E-1317 at Y, witness=13. Validated in 68 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.