Let's find some large sexy prime pair (and, perhaps, a triplet)

[Batalov]

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

And didn't take "nearly 10 years" to beat, just ~ a day.
(153528880*(1369*2^46028-1)+6)*37*2^23014+5
(153528880*(1369*2^46028-1)+6)*37*2^23014-1

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

[paulunderwood]

Originally Posted by Batalov

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

And didn't take "nearly 10 years" to beat, just ~ a day.
(153528880*(1369*2^46028-1)+6)*37*2^23014+5
(153528880*(1369*2^46028-1)+6)*37*2^23014-1

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

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

[Puzzle-Peter]

Originally Posted by R. Gerbicz

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: https://primes.utm.edu/bios/page.php?id=3934 . That handle this problem also, I'll give how to feed this problem for the code.

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.

[paulunderwood]

./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)

./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)

My first sexy pair, based on a the 1993 Harvey Dubner prime 883*2^8922+1.

Note the huge variable

[paulunderwood]

Originally Posted by Puzzle-Peter

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.

Off-topic: Indeed! Congrats for 425521077* 2^3321910 - 1 (1,000,004 digits)

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

[Batalov]

Originally Posted by paulunderwood

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

Which also beats the 19,503-digit 'sexy' from primepairs.com , but not the current WR.

[Batalov]

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

(187983281*2^51478+4)*(5*2^51478-1)+5
(187983281*2^51478+4)*(5*2^51478-1)-1
(31,002 decimal digits)

[paulunderwood]

Originally Posted by Batalov

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

(187983281*2^51478+4)*(5*2^51478-1)+5
(187983281*2^51478+4)*(5*2^51478-1)-1
(31,002 decimal digits)

Congrats, Serge

I am searching for a sexy prime triplet. Do you care to outdo my efforts?

[rudy235]

Originally Posted by Batalov

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

(187983281*2^51478+4)*(5*2^51478-1)+5
(187983281*2^51478+4)*(5*2^51478-1)-1
(31,002 decimal digits)

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

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

[paulunderwood]

Originally Posted by rudy235

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

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

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

/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)

[Batalov]

Originally Posted by rudy235

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

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

No need for Primo. Have a look at the N+1 for that number and note that 5*2^51478-1 is a prime.