At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help) value Description: Phi(3, - 123447524288) Verification status (*): Proven Official Comment: Generalized unique Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): L4561 : Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, LLR Decimal Digits: 5338805   (log10 is 5338804.29892426) Rank (*): 16 (digit rank is 1) Entrance Rank (*): 12 Currently on list? (*): short Submitted: 2/23/2017 02:04:25 CDT Last modified: 3/8/2017 09:05:55 CDT Database id: 123041 Status Flags: TrialDiv Score (*): 51.7663 (normalized score 2596.9942)

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 1
Subcategory: "Generalized Unique"
(archival tag id 218652, tag last modified 2017-03-06 16:20:05)

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 (23 Feb 2017): 

Starting N-1 prime test of 123447^1048576-123447^524288+1 Using generic reduction FMA3 FFT length 1920K, Pass1=320, Pass2=6K, 16 threads, a = 7 123447^1048576-123447^524288+1 may be prime, trying to compute gcd's 7^((N-1)/41149)-1 is coprime to N! 7^((N-1)/3)-1 is coprime to N! 123447^1048576-123447^524288+1 is prime! (5338805 decimal digits) Time : 187808.030 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.

field value prime_id 123041 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"Phi(3,-123447^524288)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing Phi(3,-123447^524288) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 45.31% Phi(3,-123447^524288) is prime! (1147972.7831s+0.6828s) [Elapsed time: 13.29 days] modified 2017-03-31 15:53:56 created 2017-02-23 02:13:01 id 168686