42717 · 2905792 + 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: | 42717 · 2905792 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Proof-code(s): (*): | L159 : Penne, NewPGen, Base4Sierpinski, LLR |
| Decimal Digits: | 272676 (log10 is 272675.19243321) |
| Rank (*): | 26917 (digit rank is 1) |
| Entrance Rank (*): | 120 |
| Currently on list? (*): | no |
| Submitted: | 12/20/2005 21:04:46 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Removed (*): | 2/1/2013 15:39:40 UTC |
| Database id: | 76507 |
| Status Flags: | none |
| Score (*): | 42.6417 (normalized score 0.0606) |
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.
field value prime_id 76507 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv 42717 2 905792 1 2>&1 [Elapsed time: 15.251 seconds] modified 2020-07-07 22:30:43 created 2005-12-20 21:22:01 id 81769
field value prime_id 76507 person_id 9 machine WinXP Pentium M 1.7GHz what prime notes Command: pfgw.exe -n -f -t -q"42717*2^905792+1" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 99310378 Running N-1 test using base 5 N-1: 42717*2^905792+1 8Primality testing 42717*2^905792+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 42717*2^905792+1 is prime! (11584.9140s+0.0340s) 55000/905809 [Elapsed time: 11585 seconds] modified 2020-07-07 22:30:43 created 2005-12-21 07:28:43 id 81774
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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