U(54381, 1, 19426) + U(54381, 1, 19425)

This prime's information:

Archival tags:

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Lehmer number (archivable *)

Prime on list: yes, rank 3
Subcategory: "Lehmer number"
(archival tag id 239543, tag last modified 2025-10-06 19:37:13)

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Serge Batalov writes (6 Oct 2025):  (report abuse)

This Lehmer prime number is proven using CHG with N-1 factored to 24.50% and N+1 factored to 1.40%. p20401 is proven with CM. Report is available. Here is a partial CHG(server) script log: Target "Lehm91k" has 91987 digits. Modulus provides 25.896593971553478800%. Right endpoint has 21812 digits. LLL[1, 1] for client 1 has [h, u] = [4, 1] and digits in [1, 299] LLL[1, 2] for client 2 has [h, u] = [4, 1] and digits in [1, 299] LLL[2, 1] for client 3 has [h, u] = [5, 1] and digits in [299, 2861] ... LLL[106, 2] for client 212 has [h, u] = [32, 15] and digits in [21613, 21714] LLL[107, 1] for client 213 has [h, u] = [32, 15] and digits in [21714, 21812] LLL[107, 2] for client 214 has [h, u] = [32, 15] and digits in [21714, 21812] LLL was split between 214 clients. LLL[106, 2] with [h, u]=[32, 15] took 25569 seconds on client "212". Witness=211. Good reduction. Norm/bound=0.007716693476508143341 is small. Looks GOOD. LLL[107, 1] with [h, u]=[32, 15] took 62032 seconds on client "213". Witness=5. Good reduction. Norm/bound=0.007795447449600922942 is small. Looks GOOD. LLL[107, 2] with [h, u]=[32, 15] took 29627 seconds on client "214". Witness=229. Good reduction. Norm/bound=0.007880720484960888687 is small. Looks GOOD. 214 LLL reductions completed in 681.9491666666666667 CPUhours. Testing a PRP called "Lehm91k". Pol[1, 1] with [h, u]=[4, 1] has ratio=1.1392563955700639431 E-378 at X, ratio=2.5379995504107024639 E-676 at Y, witness=2. Pol[2, 1] with [h, u]=[5, 1] has ratio=0.2542806231040267486 at X, ratio=8.595429185697643131 E-2564 at Y, witness=5. Pol[3, 1] with [h, u]=[5, 1] has ratio=0.16886805560997236997 at X, ratio=1.4426477198637210481 E-1282 at Y, witness=37. ... Pol[105, 2] with [h, u]=[32, 15] has ratio=0.0005544030473157306479 at X, ratio=1.9758111587654577760 E-1564 at Y, witness=47. Pol[106, 2] with [h, u]=[32, 15] has ratio=0.0006101172108903036960 at X, ratio=5.248916274872829591 E-1514 at Y, witness=211. Pol[107, 2] with [h, u]=[32, 15] has ratio=0.003191152566398583674 at X, ratio=2.9959776234489176833 E-1465 at Y, witness=229. Validated in 1129 sec.

Verification data:

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