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The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or
π( x) for x up to 100,000,000,000,000,000. 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: | 150209! + 1 |
| Verification status (*): | Proven |
| Official Comment: | Factorial |
| Proof-code(s): (*): | p3 : Dohmen, OpenPFGW |
| Decimal Digits: | 712355 (log10 is 712354.37028954) |
| Rank (*): | 498 (digit rank is 1) |
| Entrance Rank (*): | 73 |
| Currently on list? (*): | short |
| Submitted: | 10/31/2011 08:21:31 CDT |
| Last modified: | 11/3/2011 03:21:05 CDT |
| Database id: | 102627 |
| Status Flags: | none |
| Score (*): | 45.592 (normalized score 6.4455) |
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Archival tags:
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.
- Factorial primes (archivable *)
- Prime on list: yes, rank 2
Subcategory: "Factorial"
(archival tag id 213604, tag last modified 2016-07-27 01:20:35)
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 | 102627 |
| person_id | 9 |
| machine | RedHat P4 P4 |
| what | prime |
| notes | Command: /home/caldwell/client/pfgw -t -q"150209!+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 150209!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 150211
Running N-1 test using base 150217
Calling Brillhart-Lehmer-Selfridge with factored part 33.45%
150209!+1 is prime! (240480.6224s+2.6547s)
[Elapsed time: 2.78 days]
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| modified | 2011-12-27 16:48:27 |
| created | 2011-10-31 08:23:01 |
| id | 134845 |
|
| field | value |
|---|
| prime_id | 102627 |
| person_id | 9 |
| machine | Ditto P4 P4 |
| what | trial_divided |
| notes | Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 150209 ! 1 2>&1
[Elapsed time: 59234.044 seconds]
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| modified | 2011-12-27 16:48:27 |
| created | 2011-10-31 08:35:02 |
| id | 134846 |
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Query times: 0.0006 seconds to select prime, 0.0004 seconds to seek comments.
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