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Weekly Challenge 43: A Close Match

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Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

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Weekly Challenge 19: Prime Aps

Stage: 4 and 5 Short Challenge Level: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection

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.

Did you know ... ?

Explorations of arithmetic progressions of prime numbers are an ongoing subject of mathematics research.