Problems & Puzzles:
Follow up to Puzzle 687
Puzzle 687 the way Emmanuel
tried, using four non-consecutive primes and report your
Contributions came from Giovanni Resta, Emmanuel Vantiaghem & Hakan
best quadruple is 7703, 1879, 1613, 719,
the earliest one (i.e., minimal max term) that produces 18 primes.
My maximum of 16 primes is reached for
the prime quartets 3, 71, 223, 8969 and 7, 97, 709, 3217.
The bigger the range in which I take the
four primes, the smaller the number of primes among the 24
concatenations. This is not surprising for the chance a number <
x is not prime increases with x. I took a few thousands of
random chosen quartets less than 10^12 and the average number
of primes in the 24 concatenations is 1.15/24. So, I think the
record of 16 will stand a little while.
My best quartet is (3,7,41,32327) gives 17 primes.