(V(27730, 1, 16209) + 1)/(V(27730, 1, 9) + 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 239492, tag last modified 2025-09-01 22:37:12)

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Serge Batalov writes (1 Sep 2025):  (report abuse)

This Lehmer primitive part is proven using CHG with N-1 factored to 25.81% and helper prime factors (p11064, p1832, etc) proven with CM, and several c1XX cofactors factored with msieve. Ryan Propper provided multiple factorizations (ECM and CADO/msieve). Report is available. Here is a partial CHG(server) script log: Target "LehmPrim71k" has 71976 digits. Modulus provides 25.811095829626381336%. Right endpoint has 16243 digits. LLL[1, 1] for client 1 has [h, u] = [4, 1] and digits in [1, 179] LLL[2, 1] for client 2 has [h, u] = [4, 1] and digits in [179, 508] LLL[3, 1] for client 3 has [h, u] = [5, 1] and digits in [508, 2345] LLL[4, 1] for client 4 has [h, u] = [5, 1] and digits in [2345, 3264] ... LLL[107, 1] for client 107 has [h, u] = [33, 15] and digits in [16040, 16096] LLL[108, 1] for client 108 has [h, u] = [33, 15] and digits in [16096, 16148] LLL[109, 1] for client 109 has [h, u] = [33, 15] and digits in [16148, 16197] LLL[110, 1] for client 110 has [h, u] = [33, 15] and digits in [16197, 16243] LLL was split between 110 clients. 110 LLL reductions completed in ~200 CPUhours. (need ~400 GB of RAM) ... Testing a PRP called "LehmPrim71k". Pol[1, 1] with [h, u]=[4, 1] has ratio=3.869073761956830800 E-601 at X, ratio=4.465560051463927306 E-779 at Y, witness=61. Pol[2, 1] with [h, u]=[4, 1] has ratio=1.7791060371286458951 E-450 at X, ratio=4.144862895605377687 E-779 at Y, witness=7. ... Pol[108, 1] with [h, u]=[33, 15] has ratio=0.0012858314229784705081 at X, ratio=7.165881565870480742 E-788 at Y, witness=7. Pol[109, 1] with [h, u]=[33, 15] has ratio=0.0016287186350862101064 at X, ratio=8.020449106514699983 E-739 at Y, witness=83. Pol[110, 1] with [h, u]=[33, 15] has ratio=0.003006390388871691749 at X, ratio=7.945149204139685450 E-693 at Y, witness=23. Validated in 346 sec.

Verification data:

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