28628 - 17
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: | 28628 - 17 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Proof-code(s): (*): | F : Forbes |
| Decimal Digits: | 2598 (log10 is 2597.2868025888) |
| Rank (*): | 100831 (digit rank is 8) |
| Entrance Rank (*): | 3409 |
| Currently on list? (*): | no |
| Submitted: | 5/1996 |
| Last modified: | 2/4/2026 09:29:58 UTC |
| Removed (*): | 8/10/1997 20:28:33 UTC |
| Database id: | 30379 |
| Status Flags: | none |
| Score (*): | 28.2516 (normalized score 0) |
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 30379 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000294468767 -q"2^8628-17" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 2^8628-17 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000294468767
trial
Running N-1 test using base 19
Special modular reduction using FMA3 FFT length 512 on 2^8628-17
Running N+1 test using discriminant 41, base 1+sqrt(41)
Special modular reduction using FMA3 FFT length 512 on 2^8628-17
Running N+1 test using discriminant 41, base 2+sqrt(41)
Special modular reduction using FMA3 FFT length 512 on 2^8628-17
Calling N+1 BLS with factored part 63.50% and helper 0.01% (190.51% proof)
2^8628-17 is prime! (0.3556s+0.0025s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
17
23
29
43
89
113
127
197
257
353
397
617
683
2113
3137
5153
7057
8317
10781
13553
29569
50177
78233
81929
101921
110881
229153
258721
273617
1007441
12460603
15790321
34452881
119782433
375327457
869467061
2931542417
3019242689
19707683773
35532364099
43872038849
54410972897
74153335873
1405628248417
2136469147429
4363953127297
4432676798593
4981857697937
76096559910757
191755147246433
364565561997841
581283643249112959
8965960061329101601
31100269092898119731
400902887947088899681
964837888846607544573540225953
111206916097779728932051224808777
234341789260493933662402728271919
90317512080398683509507180285854441
1297662995123479965752936319854262257
7753116956093531321410584492136326016729109189
1867935023317328048519811865525337712653538206737478396129
33725933170854542422930854135636663761123331227599520852573351371057495391835351809
38449218738315469929205966725331314088065108320477713389494264194381646386092646421
11464158678831419555307566061644085...(95 digits)...13091766942851904723145020010938191
70416545132670713938539118731969064...(100 digits)...54771590043753855404907061178826433
95586664115157648895201424312079971...(135 digits)...26409035299856143333682086748762209
38915981499546385475698917751663931...(478 digits)...71851539569687392832891605321185041modified 2026-02-04 09:29:58 created 2026-02-04 09:29:53 id 187671
field value prime_id 30379 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 19 Running N+1 test using discriminant 41, base 1+sqrt(41) Primality testing 2^8628-17 [N-1/N+1, Brillhart-Lehmer-Selfridge] Calling N+1 BLS with factored part 3.89% and helper 0.01% (11.72% proof) 2^8628-17 is Fermat and Lucas PRP! (48.770000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 20:17:12 id 61766
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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