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# combining the primes

## Question

take 3 prime numbers such that they are the same distance apart form one another.

multiply all 3, add the distance. is this number always composite?

## 4 answers to this question

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Consider primes 3,5,7. Their product is 105, the distance between each is 2, so the sum of the distance and their product is 107, which is itself prime.

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ah! duh, the first most obvious example and of course I miss it. go me.

are there any other examples?

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Another example

5,11,17. Product is 935, distance is 6 and 941 is prime. As a note all instances of this property will have the numbers spaced by some multiple of 6, save the 3,5,7 instance (I think)

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And another one (was trying to develop a system to easily find them and gave up)

7, 37, 67. product is. 17353. Add distance making the prime 17383.

Edited by Nins_Leprechaun

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