Can you post me sieve with removed composite?
Thanks

Sure.

Something is very fishy with this sieve

Original sieve contains 5600 candidates, when you removed composite it has 4551 candidates.

But when I make test sieve got this

Read [COLOR=Magenta]7027[/COLOR] terms for 4*155^n+1 from NewPGen file `155.txt'.
Split 1 base 155 sequence into 45 base 155^120 subsequences.
Recognised Generalised Fermat sequence A^2+1
Using 4 Kb for the baby-steps giant-steps hashtable, maximum density 0.15.
Baby step method gen/4, giant step method new/4.
Using 128Kb for the Sieve of Eratosthenes bitmap.
Expecting to find factors for about [COLOR=Magenta]1138.47 terms.[/COLOR]
sr1sieve 1.4.5 started: 750036 <= n <= 999992, 110000000000 <= p <= 15000000000000
110173104133 | 4*155^905128+1
110259397681 | 4*155^967174+1
p=110259523441, 29853266 p/sec, 2 factors, 0.0% done, 1 sec/factor, ETA 17 Jul 23:09
sr1sieve 1.4.5 stopped: at p=110278915793 because SIGINT was received.
Found factors for 2 terms in 9.368 sec. (expected about 0.70)

7027 - 1138 ( to be at 15000000000000 as original sieve) = 5889
Can expected number of candidates be so different ? 5889 compared to 5600 (289)

[QUOTE=pepi37;405685]Something is very fishy with this sieve

Original sieve contains 5600 candidates, when you removed composite it has 4551 candidates.

But when I make test sieve got this

Read [COLOR=Magenta]7027[/COLOR] terms for 4*155^n+1 from NewPGen file `155.txt'.
Split 1 base 155 sequence into 45 base 155^120 subsequences.
Recognised Generalised Fermat sequence A^2+1
Using 4 Kb for the baby-steps giant-steps hashtable, maximum density 0.15.
Baby step method gen/4, giant step method new/4.
Using 128Kb for the Sieve of Eratosthenes bitmap.
Expecting to find factors for about [COLOR=Magenta]1138.47 terms.[/COLOR]
sr1sieve 1.4.5 started: 750036 <= n <= 999992, 110000000000 <= p <= 15000000000000
110173104133 | 4*155^905128+1
110259397681 | 4*155^967174+1
p=110259523441, 29853266 p/sec, 2 factors, 0.0% done, 1 sec/factor, ETA 17 Jul 23:09
sr1sieve 1.4.5 stopped: at p=110278915793 because SIGINT was received.
Found factors for 2 terms in 9.368 sec. (expected about 0.70)

7027 - 1138 ( to be at 15000000000000 as original sieve) = 5889
Can expected number of candidates be so different ? 5889 compared to 5600 (289)[/QUOTE]
file `155.txt' is your own file, so if anything is fishy it could be with that file.
[QUOTE=pepi37;405685]Can [U]expected[/U] number of candidates be so different ? 5889 compared to 5600 (289)[/QUOTE]
Of course it can. That's why the word "[U]expected[/U]" is used. The "[U]expected[/U]" number of candidates can be way off epecially because the estimate is for a irreducible form, while this form is algebraically reducible for a fraction of candidates.

I like that srsieve [B]does [/B]recognize the GFN form and [B]can [/B]as a result sieve faster (this is based on the fact that only primes of form 4k+1 can divide a A^2+1 form). On the other hand, srsieve does [B]not [/B]recognize Aurifeillian fraction and does not remove it - but as the closing line from 'Some Like It Hot' goes, "No one is perfect".

Thanks Batalov, so lets LLR-ing start :)
And thanks for reduce LLR time for about 60 days!

[QUOTE=Batalov;405687]I like that srsieve [B]does [/B]recognize the GFN form and [B]can [/B]as a result sieve faster (this is based on the fact that only primes of form 4k+1 can divide a A^2+1 form). On the other hand, srsieve does [B]not [/B]recognize Aurifeillian fraction and does not remove it - but as the closing line from 'Some Like It Hot' goes, "No one is perfect".[/QUOTE]

If you have a code change that I can apply to srsieve...

[QUOTE=pepi37;405688]Thanks Batalov, so lets LLR-ing start :)
And thanks for reduce LLR time for about 60 days![/QUOTE]
I ran sr1sieve for a bit to check the estimates and removed two more candidates for you:
[CODE]15189078811981 | 4*155^968110+1
[STRIKE]15239240636801 | 4*155^943524+1[/STRIKE] (already removed, because it is 4*A^4+1)
15316822815461 | 4*155^761998+1
[/CODE]

[QUOTE=rogue;405691]If you have a code change that I can apply to srsieve...[/QUOTE]
As my granddad used to say, "Це діло треба розжувати." (Got to ruminate on this one.)
Could we make some small steps?

The 4*A^4+1 recognition can be added precisely where "Recognised Generalised Fermat sequence A^2+1" is emited. Right?
At this point all n divisible by 4 should be eliminated.
This goes for other k :: (k/4) = m^4; that is, k=4, 64, ...2500...

One other simple case is when b=m^2, and k :: (k/4) = m^4; here, all even n should be eliminated. This was the case for S100 (k=64).

But to do is right, we also need to recognize cases where small factors of b can "leak" from the base power. For that, the isPower script is the prototype for many patterns. I don't remember where it was posted, so I attached a copy of it here:
[CODE]#!/usr/bin/perl -w

use Math::BigInt;

line: while(<>) { # this is a pl_remain.txt file; it has k*b^n+c lines only
next unless /^\s*(\d+)\*(\d+)\^(n|\d+)([+-])1/ && $1 && $2;
$k = Math::BigInt->new($1);
$a = Math::BigInt->new($2);
my @powers = ($4 eq '+') ? qw(3 5 7 11) : qw(2 3 5 7 11);

if($4 eq '+') {
print "Mod 0|4 Aur\t$_"
if($k==4 || $k==64 || $k==324 || $k==1024 || $k==2500 || $k==5184);
# $b = $k->copy()->bmul($a);
# print "1|4 Aur\t$_"
# if($b==4 || $b==64 || $b==324 || $b==1024 || $b==2500 || $b==5184);
# $b->bmul($a);
# print "2|4 Aur\t$_"
# if($b==4 || $b==64 || $b==324 || $b==1024 || $b==2500 || $b==5184);
# $b->bmul($a);
# print "3|4 Aur\t$_"
# if($b==4 || $b==64 || $b==324 || $b==1024 || $b==2500 || $b==5184);
}
foreach $m (@powers) {
$b = $k->copy()->broot($m);
if ($b->copy()->bpow($m) == $k) {
if ($a->copy()->broot($m)->bpow($m) == $a) {
print "* x^$m\t$_";
next line;
}
print "Mod 0($m) $b^$m\t$_";
}
}
for ($n=1; $n<$powers[$#powers]; $n++) {
$k->bmul($a);
foreach $m (@powers) {
next if $n>=$m;
$b = $k->copy()->broot($m);
print "Mod $n($m) $b^$m\t$_" if ($b->copy()->bpow($m) == $k);
}
}
}
[/CODE]
I don't know how easy it would be to implement the same rules in sr*sieve.

[QUOTE=Batalov;405722]I ran sr1sieve for a bit to check the estimates and removed two more candidates for you:
[CODE]15189078811981 | 4*155^968110+1
[STRIKE]15239240636801 | 4*155^943524+1[/STRIKE] (already removed, because it is 4*A^4+1)
15316822815461 | 4*155^761998+1
[/CODE][/QUOTE]

Thanks 2.5 hours less :)
What is removal rate if I may ask?

[QUOTE=pepi37;405725]Thanks [B]2.5 hours less[/B] :)
What is removal rate if I may ask?[/QUOTE]
It is slow, about the same as LLR. I'd say this sieve depth is just right.

I sieved on 4 cores, 0.1P interval each (that's from 15.0P to 15.4P); each took ~1.1 hour. And as you can see, 2 factors were removed (we don't count the third, because you can assume that it is [B]not [/B]in the sieve, already; I simply left n divisible by 4 in the input file).
That's 1 factor / [B]2.2 hours[/B]. So just proceed with LLR.

[QUOTE=Batalov;405726]It is slow, about the same as LLR. I'd say this sieve depth is just right.

I sieved on 4 cores, 0.1P interval each (that's from 15.0P to 15.4P); each took ~1.1 hour. And as you can see, 2 factors were removed (we don't count the third, because you can assume that it is [B]not [/B]in the sieve, already; I simply left n divisible by 4 in the input file).
That's 1 factor / [B]2.2 hours[/B]. So just proceed with LLR.[/QUOTE]

Yes, 34 candidates is already done :)
Small step for humankind, huge step for me :)