9 · 23497442 + 1
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:||9 · 23497442 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat, divides GF(3497441,10)|
|Unofficial Comments:||This prime has 2 user comments below.|
|Proof-code(s): (*):||L1780 : Ming, PSieve, Srsieve, PrimeGrid, LLR|
|Decimal Digits:||1052836 (log10 is 1052835.9043375)|
|Rank (*):||656 (digit rank is 1)|
|Entrance Rank (*):||51|
|Currently on list? (*):||short|
|Submitted:||10/24/2012 19:11:32 CDT|
|Last modified:||1/13/2014 16:20:03 CDT|
|Score (*):||46.791 (normalized score 8.654)|
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 Fermat (archivable *)
- Prime on list: no, rank 137
Subcategory: "Generalized Fermat"
(archival tag id 217581, tag last modified 2022-09-24 15:50:10)
- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: yes, rank 2, weight 48.988233326729
Subcategory: "Divides GF(*,10)"
(archival tag id 217582, tag last modified 2021-02-18 04:50:24)
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 109930 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 9 2 3497442 1 2>&1 [Elapsed time: 11.249 seconds] modified 2020-07-07 17:30:23 created 2012-10-24 19:18:01 id 149651
field value prime_id 109930 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"9*2^3497442+1" 2>&1 PFGW Version 22.214.171.124BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 9*2^3497442+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 9*2^3497442+1 is prime! (23500.7325s+0.0024s) [Elapsed time: 6.53 hours] modified 2020-07-07 17:30:23 created 2012-10-24 19:38:02 id 149652