Phi(283, - 10000)
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(283, - 10000) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Unique |
| Proof-code(s): (*): | C : Caldwell, Cruncher |
| Decimal Digits: | 1128 (log10 is 1127.9999565727) |
| Rank (*): | 125387 (digit rank is 1) |
| Entrance Rank (*): | 20126 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 10:38:26 UTC |
| Database id: | 51067 |
| Status Flags: | none |
| Score (*): | 25.6487 (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.
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 51067 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000002936445.txt -q"Phi(283,-10000)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(283,-10000) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000002936445.txt
trial
Running N-1 test using base 29
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3748-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 34.00%
Phi(283,-10000) is prime! (0.0390s+0.0049s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
37
101
283
1129
6299
9901
18049
45121
70313
79337
344887
485041
9127213
35121409
99990001
118710721
6578404633
3792128943527581
4855067598095567
60891291243097753
721030498171501831
1160803383934463712259
297262705009139006771611927
2246285860430986548506215527001
169905327561162104198557246291921
316362908763458525001406154038726382279
2144906157509411684424913774078958939881
1023037643093214557651333120422980213172396059301
441659454625809720192647055276257528637832621638030289
30073566270559048948142559741512708796590524703892560552659
441506346488360048482114135141919313523563714948107161215664533500695867
2377887731204762925852743951147119066491658516292086935221758265146322256742372441
27851538931791182813585932285490596...(119 digits)...69199442816537475115348268729799177modified 2026-02-04 10:38:26 created 2026-02-04 10:38:21 id 187705
field value prime_id 51067 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 29 Primality testing Phi(283,-10000) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 31 Running N+1 test using discriminant 61, base 12+sqrt(61) Calling N-1 BLS with factored part 3.90% and helper 0.03% (11.72% proof) Phi(283,-10000) is Fermat and Lucas PRP! (14.530000 seconds) modified 2003-03-25 17:23:04 created 2003-01-04 05:54:00 id 60895
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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