V(56003)
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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 databases at The Prime Pages: 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:

field (help)value
Description:V(56003)
Verification status (*):Proven
Official Comment:Lucas number
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p193 : Irvine, Broadhurst, Primo, OpenPFGW
Decimal Digits:11704   (log10 is 11703.9348169196)
Rank (*):71678 (digit rank is 1)
Entrance Rank (*):30818
Currently on list? (*):short
Submitted:6/19/2006 16:41:00 CDT
Last modified:7/7/2006 10:39:57 CDT
Database id:77992
Status Flags:none
Score (*):32.9276 (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.
Lucas Number (archivable *)
Prime on list: yes, rank 6
Subcategory: "Lucas Number"
(archival tag id 194012, tag last modified 2015-09-23 10:50:29)

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.

David Broadhurst writes (11 Sep 2014): 
BLS proof with ECPP helper primV(1,-1,28002)/(56003*31572462326809) in http://physics.open.ac.uk/~dbroadhu/cert/b56003.zip

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.
fieldvalue
prime_id77992
person_id9
machineWinXP Pent_M 1.7GHz Laptop
whatprime
notesCommand: pfgw.exe -n -tc -hhelp.txt -q"V(56003)" 2>&1
PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Reading factors from helper file help.txt
Running N-1 test using base 3
Primality testing V(56003) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Calling N-1 BLS with factored part 34.71% and helper 4.92% (109.05% proof)
V(56003) is prime! (313.0343s+0.0791s)
Running N+1 test using discriminant 17, base 1+sqrt(17)
[Elapsed time: 313 seconds]
Helper File:
2
3
3
11489
12923
56003
90481
185243
1400051
9261553801
12280217041
8626603198547
31572462326809
829174305548253830437427
36341293428919577145708038507
2127270730314753631848590301541129
113057373142533964948220795124814988053201
2727093182085627984424271137376420035190753262962003
130068830576457315825778446872622609400993687965962969
14195557511624298007089606382491832...(182 digits)...35596601305528339551641591948987769
86754297850303038757345917530131386...(3573 digits)...91871534517079807494228205790812963
2
2
2
5
79
233
521
719
859
2153
86161
135721
1648529
4312153
5516393
10365049
22513609
215583091
2563820041
15834206933
503863425829
1517456267839
81930214232177
98609734678214057
18774525092901870211
396866520074714493901
8002416558724839335293637
1677197765608926367411736822376373
591045866085042506389105054361881124597940603179391791
475420437734698220747368027166749382927701417016557193662268716376935476241
96202714977294636483288309569212306...(99 digits)...47017302423332986081577245143590421
26267767032828428935234891825451960...(106 digits)...99370484379038134362043762973377489
modified2006-07-14 06:27:04
created2006-06-20 09:15:06
id84547

fieldvalue
prime_id77992
person_id9
machineGenToo P3 400MHz
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"V(56003)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 3405768
V(56003) has no small factor.
[Elapsed time: 3.587 seconds]
modified2006-07-14 06:27:03
created2006-07-07 10:39:53
id85240

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.