Phi(3011, - 10)
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: | Phi(3011, - 10) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Unique, APR-CL assisted |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | F2 : Broadhurst, OpenPFGW, Primo, VFYPR |
| Decimal Digits: | 3010 (log10 is 3009.9586073148) |
| Rank (*): | 100058 (digit rank is 8) |
| Entrance Rank (*): | 23824 |
| Currently on list? (*): | no |
| Submitted: | 4/8/2001 20:14:15 UTC |
| Last modified: | 2/4/2026 10:27:58 UTC |
| Database id: | 29620 |
| Status Flags: | none |
| Score (*): | 28.7108 (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.
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.
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 29620 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000005472940.txt -q"Phi(3011,-10)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(3011,-10) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000005472940.txt
Prime_Testing_Warning,
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10003-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.37%
Phi(3011,-10) is prime! (0.3019s+0.0050s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
41
71
173
239
271
431
1721
3011
3613
4649
9091
57191
123551
909091
1527791
4147571
57009401
2182600451
821856609631
13403893556831
1963506722254397
102598800232111471
212057054080446499
265212793249617641
2140992015395526641
120525789336558438197
1958160200905006466091641
7306116556571817748755241
15941448420531279285653188808900471
18920435284033918144809657490533251
1458403742372587441269682405403605121
6798855735656881396055959081077830421892567
62115703652442437970564849055491434518411781791
59696333710576856484355571580317055432224667184271
1141240390081433457327371568501745249133720840602413587
41398275939670867448911914339156680381343777006826487831
50441422688391875381007541515590983...(110 digits)...89536137051068925751997547638790031
33781299214344096622678014073990188...(131 digits)...70247373718269979462963849500442241
17520889308448176299236543876085057...(169 digits)...40718711012045219107751867190380847
71587697905322741684108103463794296...(173 digits)...05304318511196326865672369231169613
31
59
821modified 2026-02-04 10:27:58 created 2026-02-04 10:27:53 id 187692
field value prime_id 29620 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 2 Primality testing Phi(3011,-10) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N-1 BLS with factored part 1.42% and helper 0.27% (4.54% proof) Phi(3011,-10) is Fermat and Lucas PRP! (112.240000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 21:42:34 id 61871
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.