Greetings,
Although this is not a question regarding mersenne primes, I thought I'd
throw this out to the readers here.
Let x be a prime number. Consider the series of numbers that take the
following form:
x, x + n, x + 2n, x + 3n, x + 4n, x + 5n, x + 6n, where n is an
even positive whole number.
In this series of seven numbers, can anyone tell me why, if ALL of these
numbers are prime, that the minimum value of n is 210 if all the terms
are _consecutive_ prime numbers?
This is not a trick question. I think it may have something to do with
210 being the product of the first four prime numbers. After all, the
first instance of six consecutive primes in an arithmetic progression
occurs with a value of 30, which is the product of the first three
primes. The first instance of four terms occurs with a value of 6.
And, if you can answer that question, how does the answer generalize to
consecutive primes in arithmetic progression when looking for longer
series? After a gap of 210 for seven terms, is the next gap, for eight
terms, 2310?
I found this stated on the web at:
http://felix.unife.it/Root/d-Mathematics/d-Number-theory/t-7-primes-in-progression
Regards,
Gary Untermeyer
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