PARI's commands

[science_man_88]

Originally Posted by 3.14159

You'd never finish, because you would be assigned a random exponent every time you closed p95.

At the moment, my interest is personal records. Currently my personal record is 77285 digits, and I'm looking for either 119000 or 257920 digits.

you realise I could write them in wordpad and use them next time I open through the test menu right lol.

[3.14159]

I have a variety of personal records for the many forms of primes:

Proth: 22147 * 2²⁵⁶⁷²⁰ + 1. (77285 digits) + Largest prime discovered thus far by me.
Fermat: None, all previously discovered.
Twin: About 96 digits.
Primorial: 466*7297#+1 (3124 digits), when k = 1; None: All previously discovered.
Factorial: When k = 1; None, all previously discovered. When k > 1:
1364 * 4200! + 1 (13399 digits)
Cofactor: p523 from 17228365081076784548444895 * 400²⁰⁰ + 1
Generalized Fermat: None, all previously discovered.
Generalized Proth: 207408 * 77906⁸¹⁹² + 1 (40078 digits)
Primorial-based proths: Where b is a primorial number:
703 * p(125)⁶⁶ + 1 (19104 digits)
Factorial-based proths: Where b is a factorial number:
12066 * 1621!² + 1 (9008 digits) + Need to improve on that.
Mersenne: None, all previously discovered.
Cullen/Woodall: All previously discovered
Generalized Cullen-Woodall: 4034 * 1500⁴⁰³⁴ + 1 (12817 digits)

[mdettweiler]

Originally Posted by 3.14159

You'd never finish, because you would be assigned a random exponent every time you closed p95.

At the moment, my interest is personal records. Currently my personal record is 77285 digits, and I'm looking for either 119000 or 257920 digits.

Originally Posted by science_man_88

you realise I could write them in wordpad and use them next time I open through the test menu right lol.

Prime95 saves its assignments in the worktodo.txt file; it also produces files labeled something like z******** (for LL tests), f******** (for factoring), etc. So as long as you shut down Prime95 correctly (Test>Exit), it will pick up exactly where you left off upon restart with no manual intervention.

Even if you don't shut it down "properly" (say, a power outage or something like that), you'll lose no more than 30 minutes of work; it updates the z*/f* files every 30 minutes automatically.

[science_man_88]

Originally Posted by mdettweiler

Prime95 saves its assignments in the worktodo.txt file; it also produces files labeled something like z******** (for LL tests), f******** (for factoring), etc. So as long as you shut down Prime95 correctly (Test>Exit), it will pick up exactly where you left off upon restart with no manual intervention.

Even if you don't shut it down "properly" (say, a power outage or something like that), you'll lose no more than 30 minutes of work; it updates the z*/f* files every 30 minutes automatically.

I realized this just saying even if that didn't happen I know how to at least restart them lol. I've actually switched to stress testing my CPU etc. make sure it can handle it any thing I can do that may optimize it would be nice I'm on a Compaq Presario SR2050NX with new ram and 4GB of ram. ATI graphics card,Pentium D processor.

[3.14159]

To help with organizing prime searches, I have the following idea: I will only seek out these types of primes:

1. Proths, where b is 2.
2. Generalized Proths, where b is any integer.
3. Factorial-based proths, where b is a factorial number.
4. Primorial-based proths, where b is a primorial number.
5. Prime-based proths, where b is a prime number.
6. Primorial, k * p(n) + 1
7. Factorial, k * n! + 1
8. Generalized Cullen/Woodall, k * b^k + 1
9. Factorial Cullen/Woodall, where b, optionally k, is a factorial number.
10. Primorial Cullen/Woodall, where b, optionally k, is a primorial number.
11. Prime-based Cullen/Woodall, where b is a prime number
12. k-b-b, numbers of the form k * b^b + 1
13. Factorial k-b-b, where b, optionally k, is a factorial number.
14. Primorial k-b-b, where b, optionally k, is a factorial number.
15. Prime-based k-b-b, where b is a prime number.
16. Number, square, and fourth, where n^1 + 1, n^2 + 1, and n^4 + 1 are all primes.
17. Cofactor, where this is the cofactor of any of the types of numbers listed here. Note: This is the most difficult find of all the forms of prime in this list.
18. General arithmetic progressions, k * n + c, where c is a prime > 10^2, where the prime is at least 2000 digits in length.
19. Obsolete-tech-proven primes, using the original PrimeForm or Proth.exe, or any other prime to prove primality of any type of prime listed here. Note: The prime must be at least 7500 digits in length. (Depends on whether or not you view Proth.exe and the original PrimeForm as obsolete.)

[3.14159]

By far, the most difficult find is #17, Cofactor.

Finding a large prime cofactor of about 6500 digits would be more impressive than finding a Generalized Proth of 65000 digits.

Correction:

Originally Posted by 3.14159

14. Primorial k-b-b, where b, optionally k, is a factorial number

Primorial* number is what was meant here.

[3.14159]

Also: Tomorrow: I'll only be looking for small primes, as I am not going to be on my main prime-finding machine.


So: Anyone else up for the challenge of posting a cofactor prime of at least 500 digits? (Note: The cofactor has to be of one of the 19 types of prime listed.)

[CRGreathouse]

Originally Posted by 3.14159

Cofactor: p523 from 17228365081076784548444895 * 400²⁰⁰ + 1

While recognizing the difficulty of factoring vs. simply proving primality, this would usually be expressed as a 23(?)-digit cofactor rather than a 523-digit cofactor.

[CRGreathouse]

Originally Posted by 3.14159

19. Obsolete-tech-proven primes, using the original PrimeForm or Proth.exe, or any other prime to prove primality of any type of prime listed here. Note: The prime must be at least 7500 digits in length. (Depends on whether or not you view Proth.exe and the original PrimeForm as obsolete.)

I don't think I'd want to encourage people to use outdated programs...

[3.14159]

Originally Posted by CRGreathouse

While recognizing the difficulty of factoring vs. simply proving primality, this would usually be expressed as a 23(?)-digit cofactor rather than a 523-digit cofactor.

Never said the divisors had to be small:

Ex: 499685426401622224432345842654646 * 400²⁷⁰ + 1 = 882597737519322866689219866761 * p706, new cofactor record.

[3.14159]

Originally Posted by CRGreathouse

I don't think I'd want to encourage people to use outdated programs...

The whining Luddites would love to disagree. And besides, it's kind of a challenge. Prove a decent-sixed number prime, with Proth.exe. It's only 1/4th the speed of PFGW.