Problems & Puzzles: Puzzles

 Puzzle 996. A variation of Puzzle 986 In the Puzzle 986 Gennady Gusev sent the following very nice puzzle: Find a set of N numbers and expressions with them using the 4 basic arithmetic operations (+, -, *, /) and brackets, and always using the whole set of these numbers, just once each if them, that yield the longest consecutive primes starting in 2. Gennady sent solutions for two cases: a) For the first 100 primes b) for the first 1000 primes.   Mark Mammel improved the b) solution by Gennady, finding a smaller sum set of integers for this case.   Now we change a little bit the original puzzle: Find a set of N prime numbers and expressions with them using the 4 basic arithmetic operations (+, -, *, /) and brackets, and always using the whole set of these N prime numbers, just once each if them, that yield the longest consecutive primes starting in 2. Do this for at least the first 1000 primes. Q1. Find your minimal sum set of N prime numbers for obtaining at least the first 1000 primes according to the rules defined above.

During the week 11-17 April, 2020, contributions were received from Gennady Gusev.

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Gennady sent the following file with his solutions for the first 100 and the first 1000 primes.

For the first 100+ primes the set of primes base are: Set={2,3,5,7,11,13}

For the first 1000+ primes the set of primes base are: Set={2,3,7,11,19,23,37}

Can you get "better" sets than the Gennady's ones?

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