U(5387)

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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(5387)
Verification status (*):	Proven
Official Comment (*):	Fibonacci number
Proof-code(s): (*):	WM : Morain, Williams
Decimal Digits:	1126 (log₁₀ is 1125.4669330245)
Rank (*):	121878 (digit rank is 20)
Entrance Rank (*):	1327
Currently on list? (*):	short
Submitted:	1/1/1991 05:59:59 UTC
Last modified:	3/13/2023 07:43:38 UTC
Database id:	51129
Status Flags:	none
Score (*):	25.6417 (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 14
Subcategory: "Fibonacci Number"
(archival tag id 179796, 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 51129

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000012255411 -q"U(5387)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing U(5387) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000012255411
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 53.29% and helper 50.99% (210.94% proof)

U(5387) is prime! (0.9015s+0.0010s)
[Elapsed time: 1.00 seconds]

Helper File:
2
2693
369079
759709
53402191
66231540964081
10003891161597271
332169666981841732921
72195777446499975249912346541
311680756181475991522861299701
321847098773114298393006944369
824345650181758925250079965109
2250635393569485855423798723804779449
2878991480608015596652210757176826356560238921853
26691743354749759983039892074738596990046892427030183126521175594489697658536289
30617199924845450305543138480837172...(94 digits)...74799321571238149015933442805665949
35262412696802700051313726137374425...(151 digits)...17218355969364991372623703815856261
3
5387
48473
53881
86209
2315981
4757737522158207417831995569
44428193635116460811498023883
586265643322189978969300738250123986390835156179603
11132454844151806408555772816639999...(104 digits)...86007426028007925804672486364060529
16571070946039852205938527402988540...(339 digits)...54649313420837089650040876725144363

modified 2023-03-13 07:43:38

created 2023-03-13 07:43:37

id 181571

field	value
prime_id	51129
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000012255411 -q"U(5387)" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing U(5387) [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper.php?id=1000000000012255411 Running N-1 test using base 3 Running N-1 test using base 5 Running N+1 test using discriminant 11, base 1+sqrt(11) Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N-1 BLS with factored part 53.29% and helper 50.99% (210.94% proof) U(5387) is prime! (0.9015s+0.0010s) [Elapsed time: 1.00 seconds] Helper File: 2 2693 369079 759709 53402191 66231540964081 10003891161597271 332169666981841732921 72195777446499975249912346541 311680756181475991522861299701 321847098773114298393006944369 824345650181758925250079965109 2250635393569485855423798723804779449 2878991480608015596652210757176826356560238921853 26691743354749759983039892074738596990046892427030183126521175594489697658536289 30617199924845450305543138480837172...(94 digits)...74799321571238149015933442805665949 35262412696802700051313726137374425...(151 digits)...17218355969364991372623703815856261 3 5387 48473 53881 86209 2315981 4757737522158207417831995569 44428193635116460811498023883 586265643322189978969300738250123986390835156179603 11132454844151806408555772816639999...(104 digits)...86007426028007925804672486364060529 16571070946039852205938527402988540...(339 digits)...54649313420837089650040876725144363
modified	2023-03-13 07:43:38
created	2023-03-13 07:43:37
id	181571

field value

prime_id 51129

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 3 Primality testing U(5387) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N+1 BLS with factored part 1.71% and helper 0.37% (5.54% proof) U(5387) is Fermat and Lucas PRP! (20.250000 seconds)

modified 2003-03-25 17:23:04

created 2003-01-04 05:53:35

id 60893

field	value
prime_id	51129
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 3 Primality testing U(5387) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N+1 BLS with factored part 1.71% and helper 0.37% (5.54% proof) U(5387) is Fermat and Lucas PRP! (20.250000 seconds)
modified	2003-03-25 17:23:04
created	2003-01-04 05:53:35
id	60893

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