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.

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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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