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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:
| field (help) | value |
|---|
| Description: | 489 · 2704557 + 1 |
| Verification status (*): | Proven |
| Official Comment: | |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | L689 : Brown1, Srsieve, PrimeGrid, LLR |
| Decimal Digits: | 212096 (log10 is 212095.47996389) |
| Rank (*): | 23244 (digit rank is 1) |
| Entrance Rank (*): | 1019 |
| Currently on list? (*): | no |
| Submitted: | 1/31/2010 20:14:19 CDT |
| Last modified: | 2/7/2010 19:11:32 CDT |
| Removed (*): | 2/19/2012 08:50:08 CDT |
| Database id: | 91605 |
| Status Flags: | none |
| Score (*): | 41.8689 (normalized score 0.1004) |
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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.
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 | 91605 |
| person_id | 9 |
| machine | RedHat P4 P4 |
| what | trial_divided |
| notes | Command: /home/caldwell/client/TrialDiv/TrialDiv -q 489 2 704557 1 2>&1
[Elapsed time: 9.737 seconds]
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| modified | 2011-12-27 16:48:40 |
| created | 2010-01-31 20:18:01 |
| id | 112585 |
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| field | value |
|---|
| prime_id | 91605 |
| person_id | 9 |
| machine | RedHat P4 P4 |
| what | prime |
| notes | Command: /home/caldwell/client/pfgw -t -q"489*2^704557+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 489*2^704557+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(98304,20) to FFT(98304,19)
Reduced from FFT(98304,19) to FFT(98304,18)
Reduced from FFT(98304,18) to FFT(98304,17)
Reduced from FFT(98304,17) to FFT(98304,16)
1409140 bit request FFT size=(98304,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
489*2^704557+1 is prime! (-1279.9873s+0.0000s)
[Elapsed time: 50.57 minutes]
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| modified | 2010-03-13 18:56:31 |
| created | 2010-01-31 20:23:02 |
| id | 112586 |
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Query times: 0.0007 seconds to select prime, 0.0008 seconds to seek comments.
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