465859^2097152 - 465859^1048576 + 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.

Generalized Unique (archivable *)

Prime on list: yes, rank 2
Subcategory: "Generalized Unique"
(archival tag id 228727, tag last modified 2023-12-14 08:37:23)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Serge Batalov writes (1 Jun 2023):  (report abuse)

Also can be written as: 465859^2097152-465859^1048576+1 = (465859^1048576-1)*465859^1048576+1 to demonstrate that Pocklington N-1 primality test as implemented in LLR is applicable. N-1 proof with LLR is performed externally (using multiple a values, and on different hardware). For additional validation and to avoid software bias, PRP tests are adding different s/w (Prime95) using mulitple bases . Finally, Cyclo gproof is available (though this is yet not a widely recognized format). Starting N-1 prime test of 465859^2097152-465859^1048576+1 Base factorized as : 199*2341 Base prime factor(s) taken : 199, 2341 Input matches Phi(3,-465859^1048576) - all-complex FFT length 3*2^20 is applicable. Using all-complex AVX-512 FFT length 3M, Pass1=192, Pass2=16K, clm=4, 24 threads, a = 11 465859^2097152-465859^1048576+1 may be prime, trying to compute gcd's 11^((N-1)/2341)-1 is coprime to N! 11^((N-1)/199)-1 is coprime to N! 465859^2097152-465859^1048576+1 is prime! (11887192 decimal digits) Time : 49687.570 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.