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'Weekly Challenge 19: Prime Aps' printed from http://nrich.maths.org/
Show that if three prime numbers, all greater than 3, form an
arithmetic progression then the common difference of the
progression is divisible by 6.
Find some examples of three primes which include the number 3 and
form an AP, and show that in every such case the common difference
is not divisible by 6.
know ... ?
Explorations of arithmetic progressions of prime numbers are an
ongoing subject of mathematics research.