(114801 - 1)/10
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: | (114801 - 1)/10 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized repunit, APR-CL assisted |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | F2 : Broadhurst, OpenPFGW, Primo, VFYPR |
| Decimal Digits: | 4999 (log10 is 4998.7262814446) |
| Rank (*): | 95015 (digit rank is 1) |
| Entrance Rank (*): | 18770 |
| Currently on list? (*): | no |
| Submitted: | 12/9/2000 08:44:39 UTC |
| Last modified: | 1/27/2026 09:50:18 UTC |
| Database id: | 25536 |
| Status Flags: | none |
| Score (*): | 30.2883 (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.
- APR-CL assisted (tolerated *)
- Prime on list: no, rank 2
Subcategory: "APR-CL assisted"
(archival tag id 195240, tag last modified 2023-03-11 15:53:59)- Generalized Repunit (archivable *)
- Prime on list: no, rank 129
Subcategory: "Generalized Repunit"
(archival tag id 195239, tag last modified 2025-09-11 16:37:14)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 25536 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000213510587 -q"(11^4801-1)/10" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (11^4801-1)/10 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000213510587
trial
Running N-1 test using base 23
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 16606-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 16606-bit number
Running N-1 test using base 43
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 16606-bit number
Running N+1 test using discriminant 53, base 10+sqrt(53)
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 16606-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 40/16620 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 53, base 10+sqrt(53)
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 16606-bit number
Calling N-1 BLS with factored part 37.55% and helper 0.07% (112.74% proof)
(11^4801-1)/10 is prime! (4.3211s+0.0015s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
17
19
31
37
41
61
97
101
151
193
241
257
401
577
601
641
751
1117
1201
1601
1777
2081
2689
3001
3121
3221
3361
4001
4801
5281
7321
7681
9601
10657
13421
20113
24151
46601
51329
85201
90001
96001
114001
225601
232961
241601
299401
497281
850177
2254601
4801921
6304673
7537711
7746049
18278401
49350401
59302051
195019441
212601841
699684001
980404801
1106131489
1698371041
1826934301
1947638401
5931105001
23081489281
27903093601
52020741601
69084589801
125797742401
447600088289
1856458657451
2248313994601
5880599874001
10628056841921
23417174889601
35704203336001
291281336764801
295090738600481
302956332083401
780571892394001
1037593750081121
1120648576818041
12352868954187841
13928006777524033
14436295738510501
27601683227493601
46329453543600481
69220917578031208961
7884604271247668072701
11710273559942897538241
12658046117876244394801
27665283091695977275201
40589999671017742452961
504562013892511955344201
16625767615199325017280401
582814264781738783702162161
1993099906542710819727884501
21283620033217629539178799361
399806412551699044818733915681
3659233404740477018363752843393
2012875525822725447651340174136551
18074341630577348555429415775408321
402968902472395360889178149434861784137338065281
896720806439075722628289609391420338234464212801
5940971080791781475205231741333726630941085795712801
552947563691215268017880199633798414702158479175508601
25979746658107161913187074671032833320672752745552382077035701
107357077064870190472106220245376611988014765191254292138956845448754328801
29506777999036860057952321986485794343221557168398961878003734201596625828321
11973785103580380667080002541762950...(96 digits)...19074894272609324691246093283528961
20969848996470245049588245044094528...(101 digits)...93756256456829799135506061476961001
17777131777379061091364634210158654...(251 digits)...68711464422979426358747029572080001
1901modified 2026-01-27 09:50:18 created 2026-01-27 09:50:13 id 187592
field value prime_id 25536 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000213510587 -q"(11^4801-1)/10" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (11^4801-1)/10 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000213510587
trial
Running N-1 test using base 23
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 16606-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 16606-bit number
Running N-1 test using base 43
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 16606-bit number
Running N+1 test using discriminant 53, base 10+sqrt(53)
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 16606-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 39/16620 ERROR: ROUND OFF 0.45722>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 53, base 10+sqrt(53)
Generic modular reduction using generic reduction AVX-512 FFT length 2K on A 16606-bit number
Calling N-1 BLS with factored part 37.55% and helper 0.07% (112.74% proof)
(11^4801-1)/10 is prime! (1.9251s+0.0008s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
17
19
31
37
41
61
97
101
151
193
241
257
401
577
601
641
751
1117
1201
1601
1777
2081
2689
3001
3121
3221
3361
4001
4801
5281
7321
7681
9601
10657
13421
20113
24151
46601
51329
85201
90001
96001
114001
225601
232961
241601
299401
497281
850177
2254601
4801921
6304673
7537711
7746049
18278401
49350401
59302051
195019441
212601841
699684001
980404801
1106131489
1698371041
1826934301
1947638401
5931105001
23081489281
27903093601
52020741601
69084589801
125797742401
447600088289
1856458657451
2248313994601
5880599874001
10628056841921
23417174889601
35704203336001
291281336764801
295090738600481
302956332083401
780571892394001
1037593750081121
1120648576818041
12352868954187841
13928006777524033
14436295738510501
27601683227493601
46329453543600481
69220917578031208961
7884604271247668072701
11710273559942897538241
12658046117876244394801
27665283091695977275201
40589999671017742452961
504562013892511955344201
16625767615199325017280401
582814264781738783702162161
1993099906542710819727884501
21283620033217629539178799361
399806412551699044818733915681
3659233404740477018363752843393
2012875525822725447651340174136551
18074341630577348555429415775408321
402968902472395360889178149434861784137338065281
896720806439075722628289609391420338234464212801
5940971080791781475205231741333726630941085795712801
552947563691215268017880199633798414702158479175508601
25979746658107161913187074671032833320672752745552382077035701
107357077064870190472106220245376611988014765191254292138956845448754328801
29506777999036860057952321986485794343221557168398961878003734201596625828321
11973785103580380667080002541762950...(96 digits)...19074894272609324691246093283528961
20969848996470245049588245044094528...(101 digits)...93756256456829799135506061476961001
17777131777379061091364634210158654...(251 digits)...68711464422979426358747029572080001
1901modified 2024-11-22 08:19:47 created 2024-11-22 08:19:42 id 184614
field value prime_id 25536 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing Reading factors from helper file helper Running N-1 test using base 23 7466575723...0369148801 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N-1 test using base 43 Running N+1 test using discriminant 53, base 10+sqrt(53) Calling N-1 BLS with factored part 3.58% and helper 0.07% (10.81% proof) (11^4801-1)/10 is Fermat and Lucas PRP! (427.390000 seconds) modified 2003-03-25 17:22:46 created 2003-01-07 19:43:20 id 64175
Query times: 0.0004 seconds to select prime, 0.0019 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.