phil1882 Posted December 29, 2013 Report Share Posted December 29, 2013 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? Quote Link to comment Share on other sites More sharing options...
0 ThunderCloud Posted December 29, 2013 Report Share Posted December 29, 2013 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. Quote Link to comment Share on other sites More sharing options...
0 phil1882 Posted December 30, 2013 Author Report Share Posted December 30, 2013 ah! duh, the first most obvious example and of course I miss it. go me. are there any other examples? Quote Link to comment Share on other sites More sharing options...
0 Nins_Leprechaun Posted December 30, 2013 Report Share Posted December 30, 2013 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) Quote Link to comment Share on other sites More sharing options...
0 Nins_Leprechaun Posted December 30, 2013 Report Share Posted December 30, 2013 (edited) 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 December 30, 2013 by Nins_Leprechaun Quote Link to comment Share on other sites More sharing options...
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phil1882
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?
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