PARI's commands - Page 84

3.14159 · 2010-08-26, 20:06

Quote:

Originally Posted by CRGreathouse

I grant that there are people who would consider either reasonable. My statement holds for both definitions, and indeed a wider range on both sides.

Sieving efficiency doesn't improve much when one goes deeper than about 10¹² or so.

Quote:

Originally Posted by CRGreathouse

If you're interested, go ahead. I'd rather spend the time looking up better estimates of the product (with or without the assumption of the RH).

It was merely a suggestion. I do not intend on doing so.

CRGreathouse · 2010-08-26, 20:08

Quote:

Originally Posted by 3.14159

Well, I sieved to 700M. Apparently, there are still a load of candidates left.

Code:

ff(x)=1/log(x)/exp(Euler)
s=ff(700e6);forprime(p=2,90,s*=p/(p-1));s

CRGreathouse · 2010-08-26, 20:10

Quote:

Originally Posted by 3.14159

Sieving efficiency doesn't improve much when one goes deeper than about 10¹² or so.

Code:

> ff(1e12)/ff(1e9)
%1 = 0.7500000000000000000000000000

so going to 1e12 only removes about a quarter of the candidates left at 1e9.

3.14159 · 2010-08-26, 20:15

Quote:

Originally Posted by CRGreathouse

Well, I sieved to 700M. Apparently, there are still a load of candidates left.

I was not making a reference to p(90); I was referring to 1621!²

CRGreathouse · 2010-08-26, 20:27

Quote:

Originally Posted by 3.14159

I was not making a reference to p(90); I was referring to 1621!²

In that case,

Code:

s=ff(700e6);forprime(p=2,1621,s*=p/(p-1));s
%1 = 0.3648162081214616551560298255

so about 5/8 of the candidates should be removed by sieving up to 700 million. To get to 2/3 you'd need 5 billion...

3.14159 · 2010-08-26, 20:47

Well, I found a PRP somewhat soon: 12066 * 1621!² + 1

3.14159 · 2010-08-26, 21:58

Record project: k * 15670! + 1 (≈59k digits)

k-range: 100k to 330k.

Odds: 1 in 7880 with no sieving. With sieving to 1.5*10⁹, about 1 in 3900 to 4500, assuming 1/2 of candidates are eliminated.

Sieving should take 5-10 minutes.

3.14159 · 2010-08-26, 22:20

This is taking somewhat longer than I thought. I canceled and went for a smaller range after 33 minutes of nothing.

I'm going to settle between 50 and 100 million.

3.14159 · 2010-08-27, 00:35

Settled for 315 million, testing: The odds are about 1 in 3890. So I expect a prime in 3890 * 4 minutes, or 1556 minutes, or within 26 hours.

3.14159 · 2010-08-27, 01:47

Okay: I sieved for k * 48⁷⁸⁹⁰ + 1 and k * 1296⁵⁶⁸⁰ + 1 (Correction, still sieving for the latter. Up to 193 billion)

3.14159 · 2010-08-27, 02:26

I have an idea: Make a variant of vk which sieves for primes in em2, where em2 is the set of integers such that n * m + 1 is divisible by a user-specified number.

Let's make a description: em2 gives the liftmod for Mod(-1, x)/(n), where n is any integer, and where x is any integer coprime to n.

em2 gives the set of integers liftmod(Mod(-1, x)/(n)) + a*x.

a will be a user-specified range, and so will the x and n for em2.

It's basically a sieve that searches for prime cofactors of k * n + 1.

Ex: 17228365081076784548444895 * 400²⁰⁰ + 1 = 45569 * 455603 * 755617 * 7757609 * p523

2010-08-26, 21:58	#920
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Record project: k * 15670! + 1 (≈59k digits) k-range: 100k to 330k. Odds: 1 in 7880 with no sieving. With sieving to 1.510⁹, about 1 in 3900 to 4500, assuming 1/2 of candidates are eliminated. Sieving should take 5-10 minutes. Last fiddled with by 3.14159 on 2010-08-26 at 21:58*

2010-08-26, 22:20	#921
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	This is taking somewhat longer than I thought. I canceled and went for a smaller range after 33 minutes of nothing. I'm going to settle between 50 and 100 million. Last fiddled with by 3.14159 on 2010-08-26 at 22:30

2010-08-27, 01:47	#923
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	Okay: I sieved for k * 48⁷⁸⁹⁰ + 1 and k * 1296⁵⁶⁸⁰ + 1 (Correction, still sieving for the latter. Up to 193 billion) Last fiddled with by 3.14159 on 2010-08-27 at 02:22

2010-08-27, 02:26	#924
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	I have an idea: Make a variant of vk which sieves for primes in em2, where em2 is the set of integers such that n * m + 1 is divisible by a user-specified number. Let's make a description: em2 gives the liftmod for Mod(-1, x)/(n), where n is any integer, and where x is any integer coprime to n. em2 gives the set of integers liftmod(Mod(-1, x)/(n)) + ax. a will be a user-specified range, and so will the x and n for em2. It's basically a sieve that searches for prime cofactors of k n + 1. Ex: 17228365081076784548444895 * 400²⁰⁰ + 1 = 45569 * 455603 * 755617 * 7757609 * p523 Last fiddled with by 3.14159 on 2010-08-27 at 03:17

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2010-08-26, 20:47	#919
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	Well, I found a PRP somewhat soon: 12066 * 1621!² + 1

2010-08-27, 00:35	#922
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	Settled for 315 million, testing: The odds are about 1 in 3890. So I expect a prime in 3890 * 4 minutes, or 1556 minutes, or within 26 hours.