U(30757)
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(30757) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Fibonacci number, cyclotomy |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p54 : Broadhurst, Water, OpenPFGW |
| Decimal Digits: | 6428 (log10 is 6427.4833661664) |
| Rank (*): | 88341 (digit rank is 3) |
| Entrance Rank (*): | 18753 |
| Currently on list? (*): | short |
| Submitted: | 7/24/2001 03:15:40 UTC |
| Last modified: | 3/13/2023 09:35:13 UTC |
| Database id: | 22126 |
| Status Flags: | Verify |
| Score (*): | 31.0691 (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 9
Subcategory: "Fibonacci Number"
(archival tag id 194818, tag last modified 2023-09-15 17:37:10)- Cyclotomy Proof (tolerated *)
- Prime on list: no, rank 79
Subcategory: "Cyclotomy Proof"
(archival tag id 194817, tag last modified 2023-03-11 15:53:59)
User comments about this prime (disclaimer):
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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 22126 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000012280781 -q"U(30757)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing U(30757) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000012280781
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 24.89% and helper 18.61% (93.28% proof)
U(30757) is Fermat and Lucas PRP! (5.4909s+0.0103s)
[Elapsed time: 6.00 seconds]
Helper File:
2
29
89
199
521
1399
9901
15377
19801
139801
2271751
5997421
34779911
383942651
818757341
6911530261
10886778211
13953397457
245701220509
25047390419633
43808435881211
596107814364089
689667151970161
46322958173926981
190858857319368811
671040394220849329
973154652853817809
143294873237500423340864041
593909757563487525368263441
1054368331594471750331096441
631484089583693149557829547141
873757179900549251563653697571
3488705745182141992253394497861
44455892420530356469398084710452679
33827068326080345178548440521093634561
7291644721114253348052048189753959744976091
30999368692860646796953658231647272519923645081
3618551401651342479399820830704480130793178810339
3565521683196754943245655497577124992129207006684416683019466576624709676217
1923100243130659262025935524037050897113836477921947443245225009915695876843171424158339
83153986518506817527063052703413130...(417 digits)...43135230076826088939556312759217181
3
13
43
233
307
337
8387
13049
30757
42589
89909
246049
668243
741469
5330597
159607993
247518413
261399601
2151992933
17387541121
33249689017
77271070969
104600155609
8347815816341
126213229732669
157037844472969321
11158064702254278353
63351148359425846737
69437671937928401952347
103126422139070703340776467
2328777348444558613065812893
8923252312625774237535172427423079233669
774059118009573470026172798150004363897927179083994209
20385226906747057231700814232361316...(93 digits)...48105413972490539593447819643138241
75634248156420950861146775345740016...(173 digits)...56905005042189169686922000057173483
56030794827424989867697422689272076...(944 digits)...76841082042118367670779802194188603modified 2023-03-13 09:35:13 created 2023-03-13 09:35:07 id 181577
field value prime_id 22126 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 3043449966...8033019655 Running N-1 test using base 3 7848363137...0492975737 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N+1 BLS with factored part 0.84% and helper 0.46% (2.98% proof) U(30757) is Fermat and Lucas PRP! (573.350000 seconds) modified 2003-03-25 17:22:44 created 2003-01-08 06:38:09 id 64462
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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