U(9677)
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: | U(9677) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Fibonacci number, ECPP |
| Proof-code(s): (*): | c2 : Water, Primo |
| Decimal Digits: | 2023 (log10 is 2022.0239096969) |
| Rank (*): | 105651 (digit rank is 99) |
| Entrance Rank (*): | 27973 |
| Currently on list? (*): | short |
| Submitted: | 11/23/2000 07:47:37 UTC |
| Last modified: | 3/13/2023 09:40:07 UTC |
| Database id: | 35537 |
| Status Flags: | Verify |
| Score (*): | 27.4713 (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.
- Fibonacci Number (archivable *)
- Prime on list: yes, rank 12
Subcategory: "Fibonacci Number"
(archival tag id 179790, tag last modified 2023-09-15 17:37:10)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 904
Subcategory: "ECPP"
(archival tag id 179789, tag last modified 2024-04-19 02:37:11)
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 35537 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000012259701 -q"U(9677)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing U(9677) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000012259701
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N+1 BLS with factored part 19.80% and helper 15.23% (74.66% proof)
U(9677) is Fermat and Lucas PRP! (0.8733s+0.0019s)
[Elapsed time: 1.00 seconds]
Helper File:
2
353
709
2789
8969
9679
59369
336419
370248451
2710260697
272291098033501
232950485593670759
2701182952780835573
7868980368484389544909
18217032265020629664995461
26916474730038548975178307157
2233691168243356522849781572351
29958621784923946751555618198011
5050155098623880471830641087177098509
114766147624034029216665560967209591179
3
163
9677
32261
800483
15247723
184923997
350207569
100049587197598387
1641153921530943821
14432515527520337751061
209631680902244738981735564196161923439211670412260025467249
28155331915618732883268212841205519...(243 digits)...56508865366286197799196588287301453modified 2023-03-13 09:40:07 created 2023-03-13 09:40:06 id 181580
field value prime_id 35537 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing U(9677) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 4+sqrt(5) Calling N-1 BLS with factored part 1.35% and helper 0.57% (4.67% proof) U(9677) is Fermat and Lucas PRP! (40.220000 seconds) modified 2003-03-25 17:22:59 created 2003-01-04 18:19:10 id 61539
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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