19 · 22206266 + 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:||19 · 22206266 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||[none]|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||p189 : Bohanon, LLR, OpenPFGW|
|Decimal Digits:||664154 (log10 is 664153.52316719)|
|Rank (*):||3906 (digit rank is 1)|
|Entrance Rank (*):||23|
|Currently on list? (*):||yes|
|Submitted:||9/15/2006 08:12:42 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||45.3769 (normalized score 1.7439)|
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 78496 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 19 2 2206266 1 2>&1 [Elapsed time: 10.265 seconds] modified 2020-07-07 22:30:42 created 2006-09-15 08:22:01 id 86090
field value prime_id 78496 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"19*2^2206266+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 19*2^2206266+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(327680,19) to FFT(327680,18) Reduced from FFT(327680,18) to FFT(327680,17) Reduced from FFT(327680,17) to FFT(327680,16) 4412550 bit request FFT size=(327680,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 19*2^2206266+1 is prime! (-482.4903s+0.0000s) [Elapsed time: 48630 seconds] modified 2020-07-07 22:30:42 created 2006-09-15 08:23:01 id 86091