Problems & Puzzles: Puzzles

Puzzle 491. Sum of any combination is not prime Anton Vrba  sent the following puzzle: Add terms to the series 4, 24, 24, 122, 332, 2487, 11847, 40196, 73915, ... 4 is the first composite number 24, 25 are the least two consecutive composite numbers whose sum is not prime 24, 25 and 26 are the least three consecutive consecutive numbers whose sum of any combination is not prime (24+25, 25+26, 24+26 and 24+25+26) 122, 123, 124 and 125 are the least four consecutive composite ......

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Contribution came fro, Igor Schein.

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Igor wrote:

The next 2 numbers are 1078046, 13865665

A few days after he added:

Going one further: 69205020.

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Farideh Firoozbakht found one more term:

The next two terms are 69205020 & 430480044.

So the first 13 terms of the sequence are:

4, 24, 24, 122, 332, 2487, 11847, 40196, 73915, 1078046, 13865665, 69205020,
430480044.

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