Problems & Puzzles: Puzzles

 Puzzle 688 Follow up to Puzzle 687 Redo Puzzle 687 the way Emmanuel tried, using four non-consecutive primes and report your best quartet.

Contributions came from Giovanni Resta, Emmanuel Vantiaghem & Hakan Summakoglu

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Giovanni wrote:

My best quadruple is 7703, 1879, 1613, 719,
the earliest one (i.e., minimal max term) that produces 18  primes.

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Emmanuel wrote:

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.

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Hakan wrote:

My best quartet is (3,7,41,32327) gives 17 primes.

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