U(34607)/13088506284255296513

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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(34607)/13088506284255296513
Verification status (*):	PRP
Official Comment (*):	Fibonacci cofactor, ECPP
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	7213 (log₁₀ is 7212.968891043)
Rank (*):	86256 (digit rank is 1)
Entrance Rank (*):	67325
Currently on list? (*):	no
Submitted:	7/1/2013 14:01:19 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	114542
Status Flags:	Verify
Score (*):	31.4269 (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.

Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 434
Subcategory: "ECPP"
(archival tag id 217196, tag last modified 2024-04-19 02:37:11)
Fibonacci cofactor (archivable *)
Prime on list: no, rank 23
Subcategory: "Fibonacci cofactor"
(archival tag id 217197, tag last modified 2024-04-19 02:37:11)

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 114542

person_id 9

machine Ditto P4 P4

what trial_divided

notes Command: /home/ditto/client/pfgw -o -f -q"U(34607)/13088506284255296513" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] U(34607)/13088506284255296513 1/1 mro=0 trial factoring to 2017693 U(34607)/13088506284255296513 has no small factor. [Elapsed time: 1.800 seconds]

modified 2020-07-07 22:30:19

created 2013-07-01 14:05:02

id 159462

field	value
prime_id	114542
person_id	9
machine	Ditto P4 P4
what	trial_divided
notes	Command: /home/ditto/client/pfgw -o -f -q"U(34607)/13088506284255296513" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] U(34607)/13088506284255296513 1/1 mro=0 trial factoring to 2017693 U(34607)/13088506284255296513 has no small factor. [Elapsed time: 1.800 seconds]
modified	2020-07-07 22:30:19
created	2013-07-01 14:05:02
id	159462

field value

prime_id 114542

person_id 9

machine WinXP Dual Core 2.6GHz 32-bit

what prp

notes Command: pfgw32.exe -tc -q"U(34607)/13088506284255296513" 2>&1 PFGW Version 3.7.3.32BIT.20130210.Win_Dev [GWNUM 27.8] Primality testing U(34607)/13088506284255296513 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.28% and helper 0.20% (1.04% proof) U(34607)/13088506284255296513 is Fermat and Lucas PRP! (15.5675s+0.0028s) [Elapsed time: 17 seconds]

modified 2020-07-07 22:30:19

created 2013-07-01 14:30:06

id 159464

field	value
prime_id	114542
person_id	9
machine	WinXP Dual Core 2.6GHz 32-bit
what	prp
notes	Command: pfgw32.exe -tc -q"U(34607)/13088506284255296513" 2>&1 PFGW Version 3.7.3.32BIT.20130210.Win_Dev [GWNUM 27.8] Primality testing U(34607)/13088506284255296513 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.28% and helper 0.20% (1.04% proof) U(34607)/13088506284255296513 is Fermat and Lucas PRP! (15.5675s+0.0028s) [Elapsed time: 17 seconds]
modified	2020-07-07 22:30:19
created	2013-07-01 14:30:06
id	159464

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