2109 · 2^3423798 - 3027 · 2⁹⁸⁸⁶⁵⁸ + 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.

Arithmetic Progressions of Primes (archivable class *)

Prime on list: yes, rank 2, weight 54.619807455939
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 227601, tag last modified 2023-03-11 16:02:32)

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Serge Batalov writes (2 Jan 2023):  (report abuse)

CH-G proof at 28.88% N-1 factored fraction. Logs follow: Primality testing 2109*2^3423798-3027*2^988658+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Generic modular reduction using generic reduction FMA3 FFT length 336K Calling Brillhart-Lehmer-Selfridge with factored part 28.88% 2109*2^3423798-3027*2^988658+1 is PRP! (8858.5509s+0.0022s) Then CHG as implemented in CHGserver package by D.Broadhurst. n=2109*2^3423798-3027*2^988658+1; F=2^988658*3^2*29*157*293; G=1; Target "AP" has 1030670 digits. Modulus provides 28.876654774149150288%. Right endpoint has 137802 digits. LLL[1, 1] for client 1 has [h, u] = [4, 1] and digits in [1, 13250] LLL[2, 1] for client 2 has [h, u] = [4, 1] and digits in [13250, 35470] LLL[3, 1] for client 3 has [h, u] = [4, 1] and digits in [35470, 50284] LLL[4, 1] for client 4 has [h, u] = [4, 1] and digits in [50284, 60159] LLL[5, 1] for client 5 has [h, u] = [5, 1] and digits in [60159, 75824] LLL[6, 1] for client 6 has [h, u] = [6, 2] and digits in [75824, 92623] ... LLL[9, 1] for client 9 has [h, u] = [6, 2] and digits in [116815, 125416] LLL[10, 1] for client 10 has [h, u] = [6, 2] and digits in [125416, 132297] LLL[11, 1] for client 11 has [h, u] = [6, 2] and digits in [132297, 137802] LLL was split between 11 clients. > gp -q -s124000000 AP3_cert.gp Testing a PRP called "AP". Pol[1, 1] with [h, u]=[4, 1] has ratio=1.29377 E-159801 at X, ratio=1.71195 E-173051 at Y, witness=5. Pol[2, 1] with [h, u]=[4, 1] has ratio=1.71195 E-173051 at X, ratio=1.65616 E-195271 at Y, witness=5. ... Pol[9, 1] with [h, u]=[6, 2] has ratio=1.84762 E-84972 at X, ratio=1.27524 E-59168 at Y, witness=5. Pol[10, 1] with [h, u]=[6, 2] has ratio=1.2752 E-59168 at X, ratio=1.50236 E-38525 at Y, witness=5. Pol[11, 1] with [h, u]=[6, 2] has ratio=1.5023 E-38525 at X, ratio=4.30251 E-22011 at Y, witness=5. Validated in 19 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.