3268739524288 - 3268739262144 + 1
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: | 3268739524288 - 3268739262144 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | p453 : Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, OpenPFGW |
| Decimal Digits: | 3415412 (log10 is 3415411.3897442) |
| Rank (*): | 155 (digit rank is 1) |
| Entrance Rank (*): | 149 |
| Currently on list? (*): | yes |
| Submitted: | 11/10/2025 16:33:16 UTC |
| Last modified: | 11/25/2025 11:37:13 UTC |
| Database id: | 141231 |
| Status Flags: | none |
| Score (*): | 50.3984 (normalized score 94.4752) |
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.
- Generalized Unique (archivable *)
- Prime on list: yes, rank 7
Subcategory: "Generalized Unique"
(archival tag id 239602, tag last modified 2026-01-03 05:37:12)
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 141231 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"3268739^524288-3268739^262144+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 3268739^524288-3268739^262144+1 [N-1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 1152K, Pass1=384, Pass2=3K, clm=2 on A 11345752-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 100444/11345752 ERROR: ROUND OFF 0.45139>0.45
(Test aborted, try again using the -a1 switch)
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 1200K, Pass1=320, Pass2=3840, clm=2 on A 11345752-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 50.00%
3268739^524288-3268739^262144+1 is prime! (512817.6449s+0.0533s)
[Elapsed time: 5.94 days]modified 2025-11-25 11:19:26 created 2025-11-19 12:52:28 id 187321
Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.