(V(6489, 1, 18903) - 1)/(V(6489, 1, 3) - 1)

This prime's information:

Archival tags:

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Lehmer primitive part (archivable *)

Prime on list: yes, rank 1
Subcategory: "Lehmer primitive part"
(archival tag id 239507, tag last modified 2025-09-17 05:37:12)

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Serge Batalov writes (16 Sep 2025):  (report abuse)

This Lehmer primitive part is proven using CHG with N-1 factored to 25.77% and helper prime factors (p11377, p878, etc) proven with CM, and several c1XX-c200 cofactors factored with msieve. Ryan Propper provided multiple factorizations (ECM and CADO/msieve). Report is available. Here is a partial CHG(server) script log (note: some steps required up to 0.8TB of RAM): Target "LehmPrim72k" has 72051 digits. Modulus provides 25.772172427521467794%. Right endpoint has 16344 digits. LLL[1, 1] for client 1 has [h, u] = [5, 1] and digits in [1, 1755] LLL[2, 1] for client 2 has [h, u] = [5, 1] and digits in [1755, 2957] LLL[3, 1] for client 3 has [h, u] = [5, 1] and digits in [2957, 3558] ... LLL[114, 1] for client 114 has [h, u] = [35, 16] and digits in [16243, 16295] LLL[115, 1] for client 115 has [h, u] = [35, 16] and digits in [16295, 16344] LLL was split between 115 clients. 115 LLL reductions completed in 175.20638888888888889 CPUhours. Testing a PRP called "LehmPrim72k". Pol[1, 1] with [h, u]=[5, 1] has ratio=1.4206438359536430380 E-651 at X, ratio=3.080018681174045757 E-2405 at Y, witness=7. Pol[2, 1] with [h, u]=[5, 1] has ratio=0.3475341231783464098 at X, ratio=3.759656678453443866 E-1203 at Y, witness=37. Pol[3, 1] with [h, u]=[4, 1] has ratio=3.928231616037414454 E-142 at X, ratio=2.8855236089096952114 E-742 at Y, witness=13. ... Pol[113, 1] with [h, u]=[35, 16] has ratio=0.0005106675678802286202 at X, ratio=1.5805160473546132598 E-893 at Y, witness=97. Pol[114, 1] with [h, u]=[35, 16] has ratio=0.00010234000951571950916 at X, ratio=4.623890263621316011 E-841 at Y, witness=263. Pol[115, 1] with [h, u]=[35, 16] has ratio=0.00023209675552088130115 at X, ratio=6.685573376960793416 E-792 at Y, witness=1279. Validated in 344 sec. A certificate was saved in file "LehmPrim72k_cert.gp".

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.