Problems & Puzzles: Puzzles

 Puzzle 883. Large three consecutive semiprimes Dmitry Kamenetsky asks for the largest known set of trio of consecutive integers that are semiprimes. Just digging around with a simple code in Ubasic I found a trio of integers of 200 digits: N-1, N & N+1 where N=10^199+10570618. For sure larger examples may be found by you. Or perhaps larger trios may have already been reported somewhere out there. Q. Send your largest example.

Contribution came from J. K. Andersen

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Andersen wrote on Jun 16, 2017:

I worked on this in 2003.
https://groups.yahoo.com/neo/groups/primenumbers/conversations/topics/11229 says:

"p=672066*4691#+1 and q=2329500*4691#+1 are primes.
p * q, 2 * (pq+1)/2, 3 * (pq+2)/3 are 4021-digit semi-primes."

Six days later (Jun 22, 2017) he added:

p=2585292*7001#+1 and q=5576994*7001#+1 are primes.
p * q, 2 * (p*q+1)/2, 3 * (p*q+2)/3 are 6032-digit semiprimes.

All prp tests and primality proofs were made with PrimeForm/GW.

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