495690450643 · 2503# + 1633050403
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: | 495690450643 · 2503# + 1633050403 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Consecutive primes arithmetic progression (5,d=30) |
| Proof-code(s): (*): | x38 : Broadhurst, OpenPFGW, Primo |
| Decimal Digits: | 1072 (log10 is 1071.9939181658) |
| Rank (*): | 124824 (digit rank is 1) |
| Entrance Rank (*): | 103523 |
| Currently on list? (*): | no |
| Submitted: | 11/20/2013 21:19:33 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 116372 |
| Status Flags: | Verify |
| Score (*): | 25.4894 (normalized score 0) |
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.
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: no, rank 13
Subcategory: "Consecutive primes in arithmetic progression (5,d=*)"
(archival tag id 217457, tag last modified 2023-03-11 15:53:59)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 745, weight 37.534483304024
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 217458, tag last modified 2023-03-11 15:53:59)
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 116372 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"495690450643*2503#+1633050403" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 495690450643*2503#+1633050403 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 5 Running N-1 test using base 7 Running N+1 test using discriminant 17, base 3+sqrt(17) Calling N-1 BLS with factored part 0.62% and helper 0.03% (1.94% proof) 495690450643*2503#+1633050403 is Fermat and Lucas PRP! (0.4922s+0.0003s) [Elapsed time: 1.00 seconds] modified 2020-07-07 22:30:18 created 2013-11-20 21:23:03 id 161879
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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