Well, I do have a detailed algorithm which may or may not speed thins up:smile:, but in short Pari-code does the sieving and if the candidates don't have small factors it writes the input file for the PFGW and launches it using the system command. I even have counter outputs for multi-threading, but at this stage the PFGW is too fast to use it. It takes longer to read and write to harddisk than finish the primality test,:smile:

[CODE]273249*6*(2^4423-1)-1 is 3-PRP! (0.0079s+0.0031s)
273249*6*(2^4423-1)+1 is 3-PRP! (0.0079s+0.0029s)
[/CODE]

Found in 10 minutes with [C]./pfgw64 -N -f mersenne_twin [/C] where mersenne_twin contains:

[CODE]ABC2 $a*6*(2^4423-1)-1 & $a*6*(2^4423-1)+1
a: from 1 to 100000000
[/CODE]

[QUOTE=paulunderwood;532327][CODE]273249*6*(2^4423-1)-1 is 3-PRP! (0.0079s+0.0031s)
273249*6*(2^4423-1)+1 is 3-PRP! (0.0079s+0.0029s)
[/CODE]

Found in 10 minutes with [C]./pfgw64 -N -f mersenne_twin [/C] where mersenne_twin contains:

[CODE]ABC2 $a*6*(2^4423-1)-1 & $a*6*(2^4423-1)+1
a: from 1 to 100000000
[/CODE][/QUOTE]

:shock:
I am still at 196998 since last night and that's for M4253.:picard:

There are ranges where sieving for small factors on PARI would be faster than PFGW, I am pretty sure.

[QUOTE=a1call;532331]:shock:
I am still at 196998 since last night and that's for M4253.:picard:

There are ranges where sieving for small factors on PARI would be faster than PFGW, I am pretty sure.[/QUOTE]

1. Just write a simple sieve using libgmp. ...or use Polysieve? it will be way faster.

2. Any number less than 10,000 digits won't be worth the paper it is written on. Why not just start with M44497 (...and that's only for a warm up) ?

[QUOTE=Batalov;532333]1. Just write a simple sieve using libgmp. ...or use Polysieve? it will be way faster.

2. Any number less than 10,000 digits won't be worth the paper it is written on. Why not just start with M44497 (...and that's only for a warm up) ?[/QUOTE]

I am aware that any twins less than 50k dd won't make it to top 10 listing, but there are 3 points. I remember I read an article somewhere that Tibetans believed that if they finish counting to some number the world would come to an end. I can't find that article but this is interesting:

[QUOTE]
if you ask a Tibetan to do finger-counting, they won't bend down one finger at a time, rather they will use their thumb to count the phalanges of the finger (the three bones that make up every digit).
[/QUOTE]
[url]https://theculturetrip.com/asia/china/articles/10-things-you-didnt-know-about-the-tibetan-language/[/url]

* There's is a value to a complete set even if it includes single digit primes.
* I am doing this as a hobby
* There is already indications towards the facts that there is a bias for small k values which is an indication for infinitude of twin primes.

Plus I have 3 cores working for the 80k Mersenne for days now and on last check they only found a single non-twin prime so far.

Thank you for the sieving tips. I will look into them.

[B]407635.6.M4253 +/- 1 [/B]are a pair of minimal Twin-Primes for [B]M4253 [/B]with 1287 dd each.

Found Using PFGW and PaulUnderwood.:smile:


ETA:
Looks like someone fed these to factorDB more than a year ago:

[url]http://factordb.com/index.php?query=407635*6*%282%5E4253-1%29%2B1+[/url]
[url]http://factordb.com/index.php?query=407635*6*%282%5E4253-1%29-1+[/url]

[QUOTE=a1call;532336][B]407635.6.M4253 +/- 1 [/B]are a pair of minimal Twin-Primes for [B]M4253 [/B]with 1287 dd each.

Found Using PFGW and PaulUnderwood.:smile:


ETA:
Looks like someone fed these to factorDB more than a year ago:

[url]http://factordb.com/index.php?query=407635*6*%282%5E4253-1%29%2B1+[/url]
[url]http://factordb.com/index.php?query=407635*6*%282%5E4253-1%29-1+[/url][/QUOTE]

[QUOTE]Primality proving
Proven by certificate
Size 202,645 bytes
Status Verified
Uploaded by Edwin Hall
Date July 4, 2012, 4:39 am[/QUOTE]

A BLS (Brillhart-Lehmer-Selfridge) proof is quicker than ECPP. This can be done by putting the [U]prime factors[/U] in a helper file:

[code]cat > mersenne_twin_4423.helper
2
3
3
3
97
113
2^4423-1
[/code]

[code]./pfgw64 -N -tp -q"273249*6*(2^4423-1)-1" -h"mersenne_twin_4423.helper"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 273249*6*(2^4423-1)-1 [N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file mersenne_twin_4423.helper
Running N+1 test using discriminant 3, base 3+sqrt(3)
273249*6*(2^4423-1)-1 is prime! (0.1872s+0.0158s)
[/code]

[code]
./pfgw64 -N -t -q"273249*6*(2^4423-1)+1" -h"mersenne_twin_4423.helper"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 273249*6*(2^4423-1)+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file mersenne_twin_4423.helper
Running N-1 test using base 2
273249*6*(2^4423-1)+1 is prime! (0.0355s+0.0001s)
[/code]

[QUOTE=paulunderwood;532337][QUOTE]

Primality proving
Proven by certificate
Size 202,645 bytes
Status Verified
Uploaded by Edwin Hall
Date July 4, 2012, 4:39 am


[/QUOTE][/QUOTE]

I have no idea where that quote is from (except that it seems to be from the "The Prime Database"), but it certainly does not seem to be from any source that is indexed by Google.

[QUOTE=a1call;532344]I have no idea where that quote is from (except that it seems to be from the "The Prime Database"), but it certainly does not seem to be from any source that is indexed by Google.[/QUOTE]

It comes from factorDB for that number.

FTR:

For [B]M9689 [/B]I rewrote my Pari-GP code so that it does sieving in Pari-GP but without multitthreading (writing out a counter where multiple instances can read a common counter ), and it is much faster to sieve in Pari and feeding it to PFGW, than running ABC2 in PFGW alone.

FTR:
I still don't know how Paul got the July 2012 information.
in this link:
[url]http://factordb.com/index.php?query=407635*6*%282%5E4253-1%29%2B1+[/url]

If i click on More information I get:
[QUOTE]
Others:
Create time
Before November 4, 2018, 12:20 am
[/QUOTE]

[QUOTE=a1call;532407]
I still don't know how Paul got the July 2012 information.
in this link:
[url]http://factordb.com/index.php?query=407635*6*%282%5E4253-1%29%2B1+[/url]

If i click on More information I get:[/QUOTE]

It seems to have vanished.