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

[rudy235]

Originally Posted by Batalov

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

Sure. But when I posted it appeared as PRP . Now it has just been changed to P (prime)

[Puzzle-Peter]

Originally Posted by paulunderwood

Congrats, Serge

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

What size are you trying to find? I might be tempted to go for it

[Puzzle-Peter]

Originally Posted by paulunderwood

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)

Thanks! I am amazed how quickly you guys learn about such news. Are you constantly monitoring the Top5000?

[paulunderwood]

Originally Posted by Puzzle-Peter

What size are you trying to find? I might be tempted to go for it

It is based on this puny number: https://www.mersenneforum.org/showpo...7&postcount=15

Please go for it!

[paulunderwood]

Originally Posted by Puzzle-Peter

Thanks! I am amazed how quickly you guys learn about such news. Are you constantly monitoring the Top5000?

You guess right. The "status page" is bookmarked.

[Batalov]

The form that I adapted from Robert's sketch allows for a separate, modified search of a triplet of uber-Primo size.

Miniscule proof-of-concept triplet:
(47172023*2^3052-4)*(5*2^2548-1)+1
(47172023*2^3052-4)*(5*2^2548-1)-3
(47172023*2^3052-4)*(5*2^2548-1)-5

Now this can be repeated for a 25K size, with a bit of compute expense. No primo proof will be needed.

Not practical to apply this construction to a quad or higher. (Quads are still of adolescent size, so proving two 10K-digit primes with Primo is less of a problem than sieve for special form and PRP for this form is slower than for a k,b,n,c form.)

[Puzzle-Peter]

8704161957*(2^20000)-1
8704161957*(2^20000)+5
8704161957*(2^20000)+11


+5 and +11 proven with PRIMO

[paulunderwood]

Originally Posted by Puzzle-Peter

8704161957*(2^20000)-1
8704161957*(2^20000)+5
8704161957*(2^20000)+11


+5 and +11 proven with PRIMO

You should update https://en.wikipedia.org/wiki/Sexy_p...prime_triplets

[Puzzle-Peter]

10409207693*(2^20000)-1
10409207693*(2^20000)+5

10409207693*(2^20000)+11


Not searching this particular form any further, so now I'll update wikipedia. Not sure about trying something a little bit bigger yet...

[paulunderwood]

According to the wiki page we now have a record quadruplet:

"n May 2019 Marek Hubal announced a 1138-digit quadruplet with p = 1567237911*2677# + 3301 + 6*n"

[Uncwilly]

Just for those that may not realise it:
Sexy primes are pairs that differ by six (sex is Latin for six).
https://en.wikipedia.org/wiki/Sexy_prime