primU(9813)

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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:	primU(9813)
Verification status (*):	Proven
Official Comment (*):	Fibonacci primitive part
Proof-code(s): (*):	DK : Dubner, Keller, Cruncher
Decimal Digits:	1367 (log₁₀ is 1366.8961125197)
Rank (*):	114735 (digit rank is 3)
Entrance Rank (*):	6126
Currently on list? (*):	no
Submitted:	7/1995
Last modified:	2/4/2026 10:30:47 UTC
Database id:	40866
Status Flags:	none
Score (*):	26.2492 (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 Primitive Part (archivable *)
Prime on list: no, rank 79
Subcategory: "Fibonacci Primitive Part"
(archival tag id 176805, tag last modified 2024-10-14 00:37:17)

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 40866

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 7872497287...2065880101 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000305583797.txt
trial

Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number
Running N-1 test using base 23
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number
Running N+1 test using discriminant 43, base 1+sqrt(43)
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number
Calling N-1 BLS with factored part 100.00% and helper 0.02% (300.07% proof)

7872497287...2065880101 is prime! (0.3130s+0.0003s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
7
11
31
61
653
1091
3271
4909
16361
25357
37061
128621
788071
1358359
1427411
1746181
2398001
3165661
802006741
827728777
967874221
1404354911
8541593161
9243609409
593985111211
1478217027041
15591491849671
32529675488417
61098860599523
8097429243052573
2203667166213063587
97389944419638836239
919046182779201475951
19516694720451630842916031
93426165620343855157636056247
21136117631534900079359940575471
773295397879261772778546122343223
3096366931907986673495271351135187
1589546141427272679433846364366380457
775837786053758555549491982006941864421
272582539819404953442962290861188918867473131
372105958732043692313735582367421470702112021
1412605384442881872089827815261929140500730381
48207334081391439649461622190959416461296653451
47634279636514802118229049910704007767073103370461
7204338025090306465053435447585274989066236336317481
13274610762728475186529036678515926243932120323278453753698141
26189356489166370464781263279425526925567119216715246292168506266430605383
659463559978912441041833334194332708211715135066644710176805982212387829759041
437956052310438876517039105267318355871253860759061276595421005151523785353065501
159700485508260784634792314459686156033620598857743119945750979800800601422426062469521
29592993019332481583203848389204198014376139473745975794672659303426088960871267359698123
99245367084589663689609996748938551...(118 digits)...03751918633022134574924653144345223

modified 2026-02-04 10:30:47

created 2026-02-04 10:30:37

id 187697

field	value
prime_id	40866
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 7872497287...2065880101 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000305583797.txt trial Running N-1 test using base 2 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number Running N-1 test using base 17 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number Running N-1 test using base 23 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number Running N-1 test using base 29 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number Running N+1 test using discriminant 43, base 1+sqrt(43) Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4541-bit number Calling N-1 BLS with factored part 100.00% and helper 0.02% (300.07% proof) 7872497287...2065880101 is prime! (0.3130s+0.0003s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 7 11 31 61 653 1091 3271 4909 16361 25357 37061 128621 788071 1358359 1427411 1746181 2398001 3165661 802006741 827728777 967874221 1404354911 8541593161 9243609409 593985111211 1478217027041 15591491849671 32529675488417 61098860599523 8097429243052573 2203667166213063587 97389944419638836239 919046182779201475951 19516694720451630842916031 93426165620343855157636056247 21136117631534900079359940575471 773295397879261772778546122343223 3096366931907986673495271351135187 1589546141427272679433846364366380457 775837786053758555549491982006941864421 272582539819404953442962290861188918867473131 372105958732043692313735582367421470702112021 1412605384442881872089827815261929140500730381 48207334081391439649461622190959416461296653451 47634279636514802118229049910704007767073103370461 7204338025090306465053435447585274989066236336317481 13274610762728475186529036678515926243932120323278453753698141 26189356489166370464781263279425526925567119216715246292168506266430605383 659463559978912441041833334194332708211715135066644710176805982212387829759041 437956052310438876517039105267318355871253860759061276595421005151523785353065501 159700485508260784634792314459686156033620598857743119945750979800800601422426062469521 29592993019332481583203848389204198014376139473745975794672659303426088960871267359698123 99245367084589663689609996748938551...(118 digits)...03751918633022134574924653144345223
modified	2026-02-04 10:30:47
created	2026-02-04 10:30:37
id	187697

field value

prime_id 40866

person_id 9

machine Linux PII 200

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Error opening file helper Running N-1 test using base 2 Primality testing primU(9813) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Calling Brillhart-Lehmer-Selfridge with factored part 2.84% primU(9813) is PRP! (7.480000 seconds)

modified 2003-03-25 17:22:48

created 2003-01-07 04:59:44

id 63845

field	value
prime_id	40866
person_id	9
machine	Linux PII 200
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Error opening file helper Running N-1 test using base 2 Primality testing primU(9813) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Calling Brillhart-Lehmer-Selfridge with factored part 2.84% primU(9813) is PRP! (7.480000 seconds)
modified	2003-03-25 17:22:48
created	2003-01-07 04:59:44
id	63845

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.