U(24, - 25, 43201)

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(24, - 25, 43201)
Verification status (*):PRP
Official Comment (*):Generalized Lucas number
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):CH12 : Propper, Batalov, OpenPFGW, Primo, CHG
Decimal Digits:60391   (log10 is 60390.991341293)
Rank (*):53417 (digit rank is 1)
Entrance Rank (*):50329
Currently on list? (*):short
Submitted:5/28/2020 13:06:44 CDT
Last modified:5/28/2020 13:20:24 CDT
Database id:130933
Status Flags:Verify, TrialDiv
Score (*):37.9995 (normalized score 0.0013)

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.
Generalized Lucas Number (archivable *)
Prime on list: yes, rank 1
Subcategory: "Generalized Lucas Number"
(archival tag id 224027, tag last modified 2020-05-28 13:20:28)

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.

Serge Batalov writes (28 May 2020):  (report abuse)
CHG with N-1 factored part 27.39% with p8022, p1749 and p849 proven with Primo

Serge Batalov writes (28 May 2020):  (report abuse)
CHG log:
27 LLL reductions completed in 23.17166 CPUhours.

Testing a PRP called "GR25".

Pol[1, 1] with [h, u]=[5, 1] has ratio=1.3947438203333904779 E-3537 at X, ratio=9.710282400930793922 E-4003 at Y, witness=19.
Pol[2, 1] with [h, u]=[5, 1] has ratio=0.012011381498205235881 at X, ratio=7.072872214406308663 E-2002 at Y, witness=5.
Pol[3, 1] with [h, u]=[4, 1] has ratio=1.4166993540848395860 E-931 at X, ratio=2.1519390303835230007 E-1931 at Y, witness=37.
Pol[4, 1] with [h, u]=[4, 1] has ratio=1.7948849863913139745 E-1549 at X, ratio=6.838511405990614113 E-1549 at Y, witness=7.
Pol[5, 1] with [h, u]=[4, 1] has ratio=3.081822505787108833 E-1299 at X, ratio=5.945713903495530753 E-1299 at Y, witness=7.
Pol[6, 1] with [h, u]=[4, 1] has ratio=1.4901327810445526821 E-1175 at X, ratio=9.085172469454626748 E-1174 at Y, witness=3.
Pol[7, 1] with [h, u]=[4, 1] has ratio=1.6594010238182715042 E-1111 at X, ratio=2.8081651141518923529 E-1111 at Y, witness=3.
Pol[8, 1] with [h, u]=[7, 2] has ratio=0.04535468740157596096 at X, ratio=6.650566543849308618 E-1871 at Y, witness=17.
Pol[9, 1] with [h, u]=[7, 2] has ratio=0.10369029896984544887 at X, ratio=1.1404174828998929225 E-1247 at Y, witness=2.
Pol[10, 1] with [h, u]=[7, 2] has ratio=0.020239731684708339181 at X, ratio=2.7974333428379746846 E-832 at Y, witness=11.
Pol[24, 1] with [h, u]=[10, 4] has ratio=1.5818670268366768043 E-371 at X, ratio=4.955145947293823957 E-813 at Y, witness=41.
Pol[25, 1] with [h, u]=[10, 4] has ratio=3.463342834088123464 E-290 at X, ratio=6.247101804200057061 E-682 at Y, witness=5.
Pol[26, 1] with [h, u]=[10, 4] has ratio=5.591683653151655665 E-216 at X, ratio=2.635109872560246711 E-565 at Y, witness=11.
Pol[27, 1] with [h, u]=[10, 4] has ratio=3.716249006526975604 E-151 at X, ratio=9.236568112847657910 E-462 at Y, witness=29.

Validated in 5 sec.

Please wait, while the certificate is saved...

A certificate was saved in file "GR25_cert.gp".

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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"lucasU(24,-25,43201)" 2>&1 PFGW Version [GWNUM 29.8] Primality testing lucasU(24,-25,43201) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 23, base 6+sqrt(23) Calling N-1 BLS with factored part 0.79% and helper 0.00% (2.38% proof) lucasU(24,-25,43201) is Fermat and Lucas PRP! (289.3121s+0.0053s) [Elapsed time: 4.83 minutes]
modified2020-07-07 17:30:10
created2020-05-28 13:11:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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