At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Verification status (*):PRP
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p414 : Naimi, OpenPFGW
Decimal Digits:1174253   (log10 is 1174252.2477249)
Rank (*):547 (digit rank is 1)
Entrance Rank (*):456
Currently on list? (*):short
Submitted:12/25/2022 05:20:43 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:134690
Blob database id:443
Status Flags:Verify
Score (*):47.1258 (normalized score 10.3659)

Description: (from blob table id=443)

This Prime is obtained by iteration of the following PARI/GP code: k = [1, 1, 1, 2, 5, 9, 6, 79, 16, 219, 580, 387, 189, 7067, 1803, 6582, 31917, 18888, 20973, 132755, 11419, 50111]; q = 2; for(i=1, #k, q = k[i] * (q - 1) * q + 1); print("n",q,"n"); Every Prime in these iterations (including the P587124) are verified to be prime via PFGW using " - tc" flag and then added to the helper file to prove the primality of the next iteration. Every prime q in these iterations can be proven via N - 1 method since all the prime factors of q - 1 are known. Please note that the PARI/GP console will run out of display buffer when "printing" the 1174253 decimal digits of this prime. You can use the "write" command to output the complete decimal integer to a file.

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.

Jeppe Stig Nielsen writes (14 May 2023):  (report abuse)
See the User comment for the previous term in this sequence, P587124. Also see OEIS A339174.

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.
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc p_134690.txt 2>&1
PFGW Version [GWNUM 29.8]
Primality testing 1768988249...5335296001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.02% proof)

1768988249...5335296001 is Fermat and Lucas PRP! (102109.4373s+2.7495s)
[Elapsed time: 28.36 hours]
modified2022-12-26 09:54:54
created2022-12-25 05:33:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.