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Mathematics
General Math
Does this imply infinite twin primes?
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[QUOTE="e2theipi2026, post: 5458576, member: 592284"] Only counting once. Twin prime counting function is counting "smaller" twin primes and twin composite version is counting "smaller" twin composites. As an example for the composite version: given 22,23,24,25,26,27 it would count every even number and include 25, but it would not count 27 because 29 is prime. So the odd composites have the real effect on the count, since all even [itex]n>2[/itex] are counted. As for proving ##p_n-f(p_n)## and ##p_n-f(p_n)## have different parity, it would come down to proving [itex]f(p_n)[/itex] changes parity infinitely many times. No proof for that at present. Not sure if I can, I will try. It would seem impossible otherwise though. The latter would imply that the number of smaller twin composites [itex]<=n[/itex] becomes always even or always odd. It would seem that what I have done is showed that the twin prime conjecture is equivalent to proving [itex]f(p_n)[/itex] changes parity infinitely many times. Thank you for responding by the way. :) [/QUOTE]
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Does this imply infinite twin primes?
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