36184 - 2
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: | 36184 - 2 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | ECPP |
| Proof-code(s): (*): | c24 : Burton, Primo |
| Decimal Digits: | 2951 (log10 is 2950.5178391864) |
| Rank (*): | 100227 (digit rank is 1) |
| Entrance Rank (*): | 26712 |
| Currently on list? (*): | no |
| Submitted: | 10/19/2001 20:16:03 UTC |
| Last modified: | 2/4/2026 08:47:50 UTC |
| Database id: | 29782 |
| Status Flags: | none |
| Score (*): | 28.6487 (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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 806
Subcategory: "ECPP"
(archival tag id 181639, tag last modified 2026-01-31 06:37:12)
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 29782 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000294641731 -q"3^6184-2" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 3^6184-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000294641731
trial
Running N-1 test using base 3
Special modular reduction using FMA3 FFT length 512 on 3^6184-2
Running N-1 test using base 7
Special modular reduction using FMA3 FFT length 512 on 3^6184-2
Running N-1 test using base 17
Special modular reduction using FMA3 FFT length 512 on 3^6184-2
Running N+1 test using discriminant 37, base 1+sqrt(37)
Special modular reduction using FMA3 FFT length 512 on 3^6184-2
Calling N+1 BLS with factored part 41.66% and helper 12.49% (137.48% proof)
3^6184-2 is prime! (0.2329s+0.0005s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
13
109
433
757
8209
24733
117798517
8047106008391
29136554299183753
32356561399076305309
284663996630519253661
634538541879036040523
193795952251956993033428990650021813
1045963705876214920796627188811335128227156263690344876782164668343294332064615217521
24438508337653102022217820583683149...(134 digits)...86561787449968750569340375244357601
5
41
9277
1182691
454333843
6259488089
1016796969359
34764123217961
14641867211654497
7175619780295897339
219067434459114063477547
650663511671253931884619
51753676317054169356502097758181015861805520123259
8011062057892989000108346044696281175092307195847153886977
3688634221782130957427547718818037277696499404785877752417789
22623573791636010835983545329917891...(185 digits)...61647732324937777879421284456892301
42604924163169206333202940175874762...(737 digits)...93032353966187187383333014145016593modified 2026-02-04 08:47:50 created 2026-02-04 08:47:45 id 187665
field value prime_id 29782 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 3 Primality testing 3^6184-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 17 Running N+1 test using discriminant 37, base 1+sqrt(37) Calling N-1 BLS with factored part 0.59% and helper 0.26% (2.06% proof) 3^6184-2 is Fermat and Lucas PRP! (115.050000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 21:20:07 id 61846
Query times: 0.0003 seconds to select prime, 0.0007 seconds to seek comments.
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