[QUOTE=Batalov;514561]No need for Primo. Have a look at the N+1 for that number and note that 5*2^51478-1 is a prime.[/QUOTE]

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

[QUOTE=paulunderwood;514553]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]

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

[QUOTE=paulunderwood;514496]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]

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

[QUOTE=Puzzle-Peter;514660]What size are you trying to find? I might be tempted to go for it[/QUOTE]

It is based on this puny number: [url]https://www.mersenneforum.org/showpost.php?p=514447&postcount=15[/url]

Please go for it!

[QUOTE=Puzzle-Peter;514663]Thanks! I am amazed how quickly you guys learn about such news. Are you constantly monitoring the Top5000?[/QUOTE]

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

Triplets, -- sky is the limit
 

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

[U]Miniscule proof-of-concept triplet:[/U]
(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.)

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


+5 and +11 proven with PRIMO

[QUOTE=Puzzle-Peter;516145]8704161957*(2^20000)-1
8704161957*(2^20000)+5
8704161957*(2^20000)+11


+5 and +11 proven with PRIMO[/QUOTE]

You should update [url]https://en.wikipedia.org/wiki/Sexy_prime#Sexy_prime_triplets[/url]

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...

According to the [URL="https://en.wikipedia.org/wiki/Sexy_prime#Sexy_prime_quadruplets"]wiki page[/URL] we now have a record quadruplet:

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

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