the next world record
 

Behold, the new world record. yay...yawn...

And didn't take "nearly 10 years" to beat, just ~ a day.
[URL="http://factordb.com/index.php?id=1100000001288370666"](153528880*(1369*2^46028-1)+6)*37*2^23014+5[/URL]
[URL="http://factordb.com/index.php?id=1100000001288370665"](153528880*(1369*2^46028-1)+6)*37*2^23014-1[/URL]

I am trying Robert's form for > 30k digits next; I like the form.

[QUOTE=Batalov;514358]Behold, the new world record. yay...yawn...

And didn't take "nearly 10 years" to beat, just ~ a day.
[URL="http://factordb.com/index.php?id=1100000001288370666"](153528880*(1369*2^46028-1)+6)*37*2^23014+5[/URL]
[URL="http://factordb.com/index.php?id=1100000001288370665"](153528880*(1369*2^46028-1)+6)*37*2^23014-1[/URL]

I am trying Robert's form for > 30k digits next; I like the form.[/QUOTE]

Drat, drat and double drat! I am searching for a ~20681 digit pair and was hoping to be the champion.

[QUOTE=R. Gerbicz;514243]That is just wrong assumption, if you'd be correct we would search only on the form say k*p#+1 and not Mersenne.

And for sieve why not use my ancient polysieve: [url]https://primes.utm.edu/bios/page.php?id=3934[/url] . That handle this problem also, I'll give how to feed this problem for the code.[/QUOTE]

Polysieve is pretty amazing. With a little bit of thinking it can do so many things and it is really fast. For some applications you need a lot of RAM though.

[CODE]./pfgw64 -t -q"5298*(1*2^8922-0)+709263602*(883*(1*2^8922-0)^2+1*2^8922-0)+1"
PFGW Version 3.7.10.64BIT.20150809.x86_Dev [GWNUM 28.7]

Primality testing 5298*(1*2^8922-0)+709263602*(883*(1*2^8922-0)^2+1*2^8922-0)+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 49.90%
5298*(1*2^8922-0)+709263602*(883*(1*2^8922-0)^2+1*2^8922-0)+1 is prime! (0.3782s+0.0001s)
[/CODE]

[CODE]./pfgw64 -t -hsexy.helper -q"5298*(1*2^8922-0)+709263602*(883*(1*2^8922-0)^2+1*2^8922-0)+7"
PFGW Version 3.7.10.64BIT.20150809.x86_Dev [GWNUM 28.7]

Primality testing 5298*(1*2^8922-0)+709263602*(883*(1*2^8922-0)^2+1*2^8922-0)+7 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file sexy.helper
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 49.94%
5298*(1*2^8922-0)+709263602*(883*(1*2^8922-0)^2+1*2^8922-0)+7 is prime! (0.3656s+0.0006s)[/CODE]

My first sexy pair, based on a the 1993 Harvey Dubner prime [URL="https://primes.utm.edu/primes/page.php?id=30139"]883*2^8922+1[/URL].

Note the huge variable :devil:

[QUOTE=Puzzle-Peter;514420]Polysieve is pretty amazing. With a little bit of thinking it can do so many things and it is really fast. For some applications you need a lot of RAM though.[/QUOTE]

Off-topic: Indeed! Congrats for [URL="https://primes.utm.edu/primes/page.php?id=126414"]425521077* 2^3321910 - 1[/URL] (1,000,004 digits) :toot:

And for the new world record for a triplet: [url]https://primes.utm.edu/primes/page.php?id=126416[/url] (20,008 digits) :toot: :toot: :toot:

[QUOTE=paulunderwood;514496]...And for the new world record for a triplet: [url]https://primes.utm.edu/primes/page.php?id=126416[/url] (20,008 digits) :toot: :toot: :toot:[/QUOTE]
Which also beats the 19,503-digit 'sexy' from primepairs.com , but [B]not [/B]the current WR. :rolleyes:

And now, the world record sexy pair with the size more appropriate for 2019:

[URL="http://factordb.com/index.php?id=1100000001289544195"](187983281*2^51478+4)*(5*2^51478-1)+5[/URL]
[URL="http://factordb.com/index.php?id=1100000001289544353"](187983281*2^51478+4)*(5*2^51478-1)-1 [/URL]
(31,002 decimal digits)

[QUOTE=Batalov;514552]And now, the world record sexy pair with the size more appropriate for 2019:

[URL="http://factordb.com/index.php?id=1100000001289544195"](187983281*2^51478+4)*(5*2^51478-1)+5[/URL]
[URL="http://factordb.com/index.php?id=1100000001289544353"](187983281*2^51478+4)*(5*2^51478-1)-1 [/URL]
(31,002 decimal digits)[/QUOTE]

Congrats, Serge :toot:

I am searching for a [URL="https://en.wikipedia.org/wiki/Sexy_prime#Sexy_prime_triplets"]sexy prime triplet[/URL]. Do you care to outdo my efforts?

[QUOTE=Batalov;514552]And now, the world record sexy pair with the size more appropriate for 2019:

[URL="http://factordb.com/index.php?id=1100000001289544195"](187983281*2^51478+4)*(5*2^51478-1)+5[/URL]
[URL="http://factordb.com/index.php?id=1100000001289544353"](187983281*2^51478+4)*(5*2^51478-1)-1 [/URL]
(31,002 decimal digits)[/QUOTE]

Question: if one of the primes is PRP [url]http://factordb.com/index.php?id=1100000001289544353[/url] Why is it considered a record?

I suppose it can be proven definitely prime with Primo if someone with the resources tries.

[QUOTE=rudy235;514559]Question: if one of the primes is PRP [url]http://factordb.com/index.php?id=1100000001289544353[/url] Why is it considered a record?

I suppose it can be proven definitely prime with Primo if someone with the resources tries.[/QUOTE]

~50% factorisation of N+1 is given by [url]https://primes.utm.edu/primes/page.php?id=11814[/url] and so leads to a quick BLS proof:

[code]/pfgw64 -tp -hsexy.helper -q"(187983281*2^51478+4)*(5*2^51478-1)-1"
PFGW Version 3.7.10.64BIT.20150809.x86_Dev [GWNUM 28.7]

Primality testing (187983281*2^51478+4)*(5*2^51478-1)-1 [N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file sexy.helper
Running N+1 test using discriminant 2, base 1+sqrt(2)
Calling Brillhart-Lehmer-Selfridge with factored part 49.99%
(187983281*2^51478+4)*(5*2^51478-1)-1 is prime! (63.8154s+0.0122s) [/code]

[QUOTE=rudy235;514559]Question: if one of the primes is PRP [url]http://factordb.com/index.php?id=1100000001289544353[/url] Why is it considered a record?

I suppose it can be proven definitely prime with Primo if someone with the resources tries.[/QUOTE]
No need for Primo. Have a look at the N+1 for that number and note that 5*2^51478-1 is a prime.