U(65181, 1, 20770) + U(65181, 1, 20769)

This prime's information:

Archival tags:

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Lehmer number (archivable *)

Prime on list: yes, rank 1
Subcategory: "Lehmer number"
(archival tag id 239525, tag last modified 2025-09-25 10:37:12)

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Serge Batalov writes (24 Sep 2025):  (report abuse)

This Lehmer prime number is proven using CHG with N-1 factored to 27.11% and N+1 factored to 1.53%. p26668=gcd(primU(65181,1,20769),lucasU(65181,1,10385)+lucasU(65181,1,10384))/835079951/15979773358837 is proven with CM. Ryan Propper provided massive PRP screening. Report is available. Here is a partial CHG(server) script log: Target "Lehmer99k" has 99985 digits. Modulus provides 28.595466308379280922%. Right endpoint has 15726 digits. LLL[1, 1] for client 1 has [h, u] = [4, 1] and digits in [1, 1382] LLL[1, 2] for client 2 has [h, u] = [4, 1] and digits in [1, 1382] LLL[2, 1] for client 3 has [h, u] = [4, 1] and digits in [1382, 3318] LLL[2, 2] for client 4 has [h, u] = [4, 1] and digits in [1382, 3318] ... LLL[16, 1] for client 31 has [h, u] = [8, 3] and digits in [14752, 15726] LLL[16, 2] for client 32 has [h, u] = [8, 3] and digits in [14752, 15726] LLL was split between 32 clients. 32 LLL reductions completed in 0.12638888888888888889 CPUhours. Testing a PRP called "Lehmer99k". Pol[1, 1] with [h, u]=[4, 1] has ratio=6.588416153674875427 E-2908 at X, ratio=2.8019309299177605588 E-4289 at Y, witness=3. Pol[2, 1] with [h, u]=[4, 1] has ratio=1.1772432977315995778 E-2353 at X, ratio=3.412127457194838157 E-4289 at Y, witness=11. ... Pol[15, 2] with [h, u]=[8, 3] has ratio=3.565801262287514974 E-1393 at X, ratio=6.221712361297948031 E-3665 at Y, witness=13. Pol[16, 2] with [h, u]=[8, 3] has ratio=0.030975925629637969454 at X, ratio=1.5793450053680898454 E-2922 at Y, witness=13. Validated in 7 sec.

Verification data:

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