A Curious Sequence of Prime Numbers

Re:A Curious Sequence of Prime Numbers by glial on Sunday May 26, 2019 @04:36PM (#20017339)

I thought it was wrong -- but looking back at Euclid's proof, Euclid doesn't specify that p_1...p_n be all the primes -- just all the known primes, so there could be gaps. He says that either

(1) -- p_1×p_2×p_3×…×p_n +1 is prime, or

(2) -- p_1×p_2×p_3×…×p_n +1 is not prime, but it's also not divisible by any of the pre-specified primes, so there must be another prime that divides into it aside from p_1...p_n.

See here: https://mathcs.clarku.edu/~djoyce/java/elements/bookIX/propI...

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Re:A Curious Sequence of Prime Numbers by _Microft on Sunday May 26, 2019 @04:40PM (#20017369)

OK, I understand. Strange that the non-successive primes are numbered with successive indices though.

PS: Well, actually not because they are not numbering all primes but numbering primes they know.

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Re:A Curious Sequence of Prime Numbers by kosievdmerwe on Sunday May 26, 2019 @09:47PM (#20018858)

Even if they are successive then the product plus one might not be prime, since the product plus one is so much larger than p_n, there might be a prime that divides it (and likely at least 2).

The first non-prime example is 2x3x5x7x11x13 + 1 which equals 59 x 509

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Re:A Curious Sequence of Prime Numbers by _Microft on Monday May 27, 2019 @02:54AM (#20019979)

Sure, see my first post about that. I amended it shortly after I posted but it felt wrong to remove the part that people responded too already.

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