PARI's commands

[3.14159]

Longest streak of trial-division-detected candidates ever seen by me:

9584 * p(65)#^40 + 1 has factors: 30869
9585 * p(65)#^40 + 1 has factors: 26237
9586 * p(65)#^40 + 1 has factors: 12959
9587 * p(65)#^40 + 1 has factors: 1831
9588 * p(65)#^40 + 1 has factors: 123853
9589 * p(65)#^40 + 1 has factors: 1511
9590 * p(65)#^40 + 1 has factors: 6701
9591 * p(65)#^40 + 1 has factors: 4723
9592 * p(65)#^40 + 1 has factors: 99103
9593 * p(65)#^40 + 1 has factors: 9091
9594 * p(65)#^40 + 1 has factors: 2207

[CRGreathouse]

Sorry, I've been sick... not quite up to my usual posting routine.

Originally Posted by 3.14159

Okay: It cannot use vectors and loops, as any method using these is dreadfully inefficient.

Sieving (with vectors) = fast, trial division = slow.

[3.14159]

Originally Posted by CRGreathouse

Sieving (with vectors) = fast, trial division = slow.

Okay: I need a decent script for that; This is well outside of my range.

I'm unsure I could complete it on my own.

[CRGreathouse]

I'll post my recent sieve; maybe you can modify it. It was the work of just a few minutes; I'm sure it could be made much more efficient.

Your sieve is variable-k which is easier to program (but you'll have to make the changes).

\\ Finding terms for A176494
sieve(lim,sz,sm=1)={
	my(v=vectorsmall(sz,i,1));
	forprime(p=3,lim,
		b=znorder(Mod(2,p));
		trap(,next,
			a=znlog(2293,Mod(2,p),b)
		);
		if(Mod(2,p)^a!=2293, print("bad at "p);next);
		a+=b*ceil((sm-a)/b);
		forstep(n=a,sz,b,
			v[n]=0
		)
	);
	a=0;
	for(i=sm,sz,if(v[i],a++;write("abc.txt", i)));
	a
};

Replace the a=0 and following lines by v (just that one character) if you want to get the vector instead of writing it to a file. This checks for terms with n = sm to n = sz, sieving out the primes up to lim.


Ugh, still sick.

[3.14159]

The only ideas I have for code are the beginning, and the end:

I require 5 arguments, not three.

(k value range; n; and primes to sieve range.)

The sieve needs to be generalized towards any arithmetic progression, I guess.

Also: The code doesn't work (Syntax error.)

Well, I'll be off to try and make the appropriate changes.

[3.14159]

Blah.. This yields no progress. I'll just give up. Endless failed ideas, with many more soon-to-be failed ideas in mind.

Well, I forfeit.

[3.14159]

Now, back to searching for general arithmetic progression primes. The odds will land me something.

(P.S: Found 5358 * 905011⁴⁷⁰ + 1 (≈ 53² digits))

Looking for k * p(125)#^66 + 1 (≈ 19100 digits)

[CRGreathouse]

Originally Posted by 3.14159

Also: The code doesn't work (Syntax error.)

That's interesting. My version says

znlog(x,g,{o}): return the discrete logarithm of x in (Z/nZ)* in base g. If
present, o represents the multiplicative order of g. If no o is given, assume
that g generate (Z/nZ)*.

but I see that my Windows version says

znlog(x,g): g as output by znprimroot (modulo a prime). Return smallest
non-negative n such that g^n = x.

so I guess you'll just have to drop that trailing ,b.

[3.14159]

The odds of finding something:

Normally: 1 in about 44000.

Potential prime factors eliminated: first 125 primes:
Leaving it at about 1 in 3750. (w/no sieving)

[CRGreathouse]

Originally Posted by 3.14159

The only ideas I have for code are the beginning, and the end:

I require 5 arguments, not three.

(k value range; n; and primes to sieve range.)

Four -- the code should probably just start at 2 or 3 for the prime range. All you need to add in terms of arguments is the n.

Originally Posted by 3.14159

The sieve needs to be generalized towards any arithmetic progression, I guess.

Changed, not generalized, from variable-n to variable-k.

[science_man_88]

CRG if you're sick take a rest or Questions will make you worse.