9 · 101585829 - 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: | 9 · 101585829 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Near-repdigit |
| Proof-code(s): (*): | A2 : Propper, Srsieve, PRST |
| Decimal Digits: | 1585830 (log10 is 1585829.9542425) |
| Rank (*): | 652 (digit rank is 1) |
| Entrance Rank (*): | 647 |
| Currently on list? (*): | yes |
| Submitted: | 5/23/2025 15:28:48 UTC |
| Last modified: | 5/27/2025 12:37:09 UTC |
| Database id: | 140779 |
| Status Flags: | none |
| Score (*): | 48.0473 (normalized score 13.0536) |
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.
- Near-repdigit (archivable *)
- Prime on list: yes, rank 9
Subcategory: "Near-repdigit"
(archival tag id 239337, tag last modified 2025-05-27 12:37:10)
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 140779 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"9*10^1585829-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 9*10^1585829-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 7, base 1+sqrt(7)
Special modular reduction using FMA3 FFT length 320K, Pass1=320, Pass2=1K, clm=4 on 9*10^1585829-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 315/5268014 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 7, base 1+sqrt(7)
Special modular reduction using FMA3 FFT length 336K, Pass1=448, Pass2=768, clm=4 on 9*10^1585829-1
Calling Brillhart-Lehmer-Selfridge with factored part 69.90%
9*10^1585829-1 is prime! (35540.8344s+0.0117s)
[Elapsed time: 9.87 hours]modified 2025-05-27 11:49:34 created 2025-05-27 01:57:11 id 186867
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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