mersenneforum.org Primality based on digital root
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 2019-02-16, 18:10 #1 neskis     Feb 2019 100002 Posts Primality based on digital root Hi! Has anyone besides me noticed this? Primes are the sum of two CONSECUTIVE integers ONLY as follows: Prime DR1 = integer DR0 + integer DR1 Prime DR2 = integer DR5 + integer DR6 Prime DR4 = integer DR6 + integer DR7 Prime DR5 = integer DR2 + integer DR3 Prime DR7 = integer DR3 + integer DR4 Prime DR8 = integer DR8 + integer DR0
 2019-02-16, 20:01 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23·5·229 Posts Yeah. And it has nothing to do with "primes". Primes in your message is a red herring. This is called modular arithmetic. Look it up. DR is nothing else than mod(9). What you are doing is: using mod(9) you are trying to solve: x + (x+1) = a (mod 9). But the solution is obvious: x = (a-1)/2 (mod 9) Example: you are saying: "DR4 = integer DR6 + integer DR7". Or in other words: "4 = 6+7 (mod 9)". That's obvious, because 6 = (4-1)/2 (mod 9). (look up how to divide by 2 in a modular system)

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