28451 - 9
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: | 28451 - 9 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Proof-code(s): (*): | F : Forbes |
| Decimal Digits: | 2545 (log10 is 2544.0044933563) |
| Rank (*): | 101498 (digit rank is 10) |
| Entrance Rank (*): | 4005 |
| Currently on list? (*): | no |
| Submitted: | 5/1996 |
| Last modified: | 2/4/2026 09:38:09 UTC |
| Removed (*): | 1996 |
| Database id: | 31024 |
| Status Flags: | none |
| Score (*): | 28.187 (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 31024 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000294468641 -q"2^8451-9" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 2^8451-9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000294468641
trial
Running N-1 test using base 11
Special modular reduction using FMA3 FFT length 512 on 2^8451-9
Running N+1 test using discriminant 19, base 1+sqrt(19)
Special modular reduction using FMA3 FFT length 512 on 2^8451-9
Running N+1 test using discriminant 19, base 2+sqrt(19)
Special modular reduction using FMA3 FFT length 512 on 2^8451-9
Calling N+1 BLS with factored part 56.75% and helper 0.85% (171.11% proof)
2^8451-9 is prime! (0.2902s+0.0002s)
[Elapsed time: 5.00 seconds]
Helper File:
2
29
271
2939
83869
1323679961
3
5
7
13
17
23
67
89
97
193
241
257
353
397
641
673
683
769
1409
2113
7393
20857
65537
229153
274177
312709
444929
599479
1258753
4327489
5304641
6700417
22253377
119782433
155852929
1632064897
1761345169
2931542417
43872038849
98618273953
1233948474881
1951050013441
15747624837121
67280421310721
190507963147393
16875081675650881
59649589127497217
18446744069414584321
46714408868623938817
441995541378330835457
5704689200685129054721
60299259845689822028046342401
349621839326921795694385454593
86945388997210442828259494992321
3046044023647117265076766795424257
44250674269198344200898981420091393
442499826945303593556473164314770689
72386545356458958441346486331202082817
155251136815444024315833387060599471617
3210843755324367119258027752661239735297
275509565477848842604777623828011666349761
331192380488114152600457428497953408512758882817
2724766004649595434157241343741767729156891206422918570211139111809
13064120070541677519355082612131650...(119 digits)...50383012729454682537615570202929281
23564925493739232585714389517039188...(125 digits)...11868864744899427472824924193932033
10669057300390045867833374036971624...(374 digits)...89507009478732645996997984581346561modified 2026-02-04 09:38:09 created 2026-02-04 09:38:04 id 187673
field value prime_id 31024 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 11 Running N+1 test using discriminant 19, base 1+sqrt(19) Running N+1 test using discriminant 19, base 2+sqrt(19) Primality testing 2^8451-9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Calling N+1 BLS with factored part 3.28% and helper 0.49% (10.36% proof) 2^8451-9 is Fermat and Lucas PRP! (76.330000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 20:02:11 id 61744
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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