# "P587124"

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:

Description: "P587124" PRP [none] This prime has 1 user comment below. p414 : Naimi, OpenPFGW 587124   (log10 is 587123.77389594) 4064 (digit rank is 1) 2273 yes 12/1/2020 02:57:53 UTC 3/11/2023 15:54:10 UTC 131431 391 Verify, TrialDiv 44.9984 (normalized score 1.2611)

#### Description: (from blob table id=391)

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]; 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

Serge Batalov writes (2 Dec 2020):  (report abuse)
 A fast way to prove automatically is to: ```gp -q k = [1, 1, 1, 2, 5, 9, 6, 79, 16, 219, 580, 387, 189, 7067, 1803, 6582, 31917, 18888, 20973, 132755, 11419]; q = 2; for(i=1, #k, q = k[i] * (q - 1) * q + 1; write("seq",q)) The file 'seq' will be its own N-1 helper. Then, run pfgw -hseq -t -l -N seq ```

#### 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.
fieldvalue
prime_id131431
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc p_131431.txt 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 5941497781...4622336001 [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% (0.03% proof) 5941497781...4622336001 is Fermat and Lucas PRP! (43259.4396s+0.8836s) [Elapsed time: 12.02 hours]
modified2021-04-20 22:39:26
created2020-12-01 03:01:02
id177124

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.