(452916381 - 1)/4528
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:||(452916381 - 1)/4528|
|Verification status (*):||PRP|
|Official Comment (*):||Generalized repunit|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||CH2 : Wu_T, OpenPFGW, Primo, CHG|
|Decimal Digits:||59886 (log10 is 59885.318108689)|
|Rank (*):||56395 (digit rank is 1)|
|Entrance Rank (*):||37433|
|Currently on list? (*):||short|
|Submitted:||12/2/2012 00:52:57 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||37.9736 (normalized score 0.001)|
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.
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.
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 110198 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(4529^16381-1)/4528" 2>&1 PFGW Version 184.108.40.206BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (4529^16381-1)/4528 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 23 Running N+1 test using discriminant 47, base 3+sqrt(47) Calling N-1 BLS with factored part 0.55% and helper 0.00% (1.65% proof) (4529^16381-1)/4528 is Fermat and Lucas PRP! (1762.7384s+0.0032s) [Elapsed time: 29.38 minutes] modified 2020-07-07 22:30:23 created 2012-12-02 00:53:01 id 150381
field value prime_id 110198 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"(4529^16381-1)/4528" 2>&1 PFGW Version 220.127.116.11BIT.20110215.x86_Dev [GWNUM 26.5] (4529^16381-1)/4528 1/1 mro=0 trial factoring to 19699746 (4529^16381-1)/4528 has no small factor. [Elapsed time: 93.624 seconds] modified 2020-07-07 22:30:23 created 2012-12-02 01:05:01 id 150382