U(9311)

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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:	U(9311)
Verification status (*):	Proven
Official Comment (*):	Fibonacci number
Proof-code(s): (*):	DK : Dubner, Keller, Cruncher
Decimal Digits:	1946 (log₁₀ is 1945.5344333654)
Rank (*):	107592 (digit rank is 1)
Entrance Rank (*):	4371
Currently on list? (*):	short
Submitted:	3/4/1995 05:59:59 UTC
Last modified:	3/13/2023 07:57:32 UTC
Database id:	37470
Status Flags:	none
Score (*):	27.351 (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 13
Subcategory: "Fibonacci Number"
(archival tag id 179791, tag last modified 2023-09-15 17:37:10)

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 37470

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000012259335 -q"U(9311)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing U(9311) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000012259335
Running N-1 test using base 17
Running N-1 test using base 31
Running N-1 test using base 41
Running N+1 test using discriminant 61, base 15+sqrt(61)
Calling N-1 BLS with factored part 58.40% and helper 21.67% (196.92% proof)

U(9311) is prime! (1.4214s+0.0066s)
[Elapsed time: 2.00 seconds]

Helper File:
2
3
7
11
23
29
47
71
191
193
389
491
911
1103
1163
1471
3299
6983
9311
9349
41611
41903
195163
391021
921889
1322021
3084989
4501963
5496409
51734341
67512001
87382901
88972241
361040209
476606831
599786069
657405169
748787341
4353947431
4716437207
4740857929
5644065667
10694421739
104164776731
459807660691
803600576327
2152958650459
75075304162951
320657355925861
56678557502141579
2350117027000544947
4959318126280687189
76674415738994499773
227993117754975870677
33213852746087495125921
248792854501527237797869
554353161797183515903106543
769701625632876440126503511
18012626151302733591167307623681
1995725302947373395780895476168743
653745898640081439497994347696773261
70841730865173768131062805045048901743
121350293508255150886076715657270663061
19057873792485795396447245757740611162172567
5302128857446935216982971462475831424585281386810339485459853126241
36950175971970115957922604034845994483295942395880687567175107225483
1062760862476640403908661258334421301159327984963376164666344786806531703
24914075541948206867377856621304229...(92 digits)...55192503445077276940670489620651407
60321138202896865542349105237349647...(126 digits)...00471348319160920540761972347942541
5
13
37
97
113
761
769
2207
3167
3457
29641
42293
141961
6168709
7123481
12326441
67735001
1655770201
21489479327
64474965673
1234548370049
351301301942501
7288331127303673
188463316368301661
127654132789883268521
417739114281337726513
31237321595326138449043487758849
128955073914024460192651484843195641
929967340482033846923210210831820066103506705843823801
40870395814374636398726174979273013...(104 digits)...41504102224414881451889765719767393

modified 2023-03-13 07:57:32

created 2023-03-13 07:57:30

id 181572

field	value
prime_id	37470
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000012259335 -q"U(9311)" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing U(9311) [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper.php?id=1000000000012259335 Running N-1 test using base 17 Running N-1 test using base 31 Running N-1 test using base 41 Running N+1 test using discriminant 61, base 15+sqrt(61) Calling N-1 BLS with factored part 58.40% and helper 21.67% (196.92% proof) U(9311) is prime! (1.4214s+0.0066s) [Elapsed time: 2.00 seconds] Helper File: 2 3 7 11 23 29 47 71 191 193 389 491 911 1103 1163 1471 3299 6983 9311 9349 41611 41903 195163 391021 921889 1322021 3084989 4501963 5496409 51734341 67512001 87382901 88972241 361040209 476606831 599786069 657405169 748787341 4353947431 4716437207 4740857929 5644065667 10694421739 104164776731 459807660691 803600576327 2152958650459 75075304162951 320657355925861 56678557502141579 2350117027000544947 4959318126280687189 76674415738994499773 227993117754975870677 33213852746087495125921 248792854501527237797869 554353161797183515903106543 769701625632876440126503511 18012626151302733591167307623681 1995725302947373395780895476168743 653745898640081439497994347696773261 70841730865173768131062805045048901743 121350293508255150886076715657270663061 19057873792485795396447245757740611162172567 5302128857446935216982971462475831424585281386810339485459853126241 36950175971970115957922604034845994483295942395880687567175107225483 1062760862476640403908661258334421301159327984963376164666344786806531703 24914075541948206867377856621304229...(92 digits)...55192503445077276940670489620651407 60321138202896865542349105237349647...(126 digits)...00471348319160920540761972347942541 5 13 37 97 113 761 769 2207 3167 3457 29641 42293 141961 6168709 7123481 12326441 67735001 1655770201 21489479327 64474965673 1234548370049 351301301942501 7288331127303673 188463316368301661 127654132789883268521 417739114281337726513 31237321595326138449043487758849 128955073914024460192651484843195641 929967340482033846923210210831820066103506705843823801 40870395814374636398726174979273013...(104 digits)...41504102224414881451889765719767393
modified	2023-03-13 07:57:32
created	2023-03-13 07:57:30
id	181572

field value

prime_id 37470

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 17 Primality testing U(9311) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 31 Running N+1 test using discriminant 41, base 12+sqrt(41) Calling N-1 BLS with factored part 3.51% and helper 1.95% (12.52% proof) U(9311) is Fermat and Lucas PRP! (51.550000 seconds)

modified 2003-03-25 17:23:00

created 2003-01-04 18:10:52

id 61517

field	value
prime_id	37470
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 17 Primality testing U(9311) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 31 Running N+1 test using discriminant 41, base 12+sqrt(41) Calling N-1 BLS with factored part 3.51% and helper 1.95% (12.52% proof) U(9311) is Fermat and Lucas PRP! (51.550000 seconds)
modified	2003-03-25 17:23:00
created	2003-01-04 18:10:52
id	61517

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.