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• ### No similar triangles in triplets of primes

A triplet of primes: (pa, p, pb) is such that d = p - pa = pb - p d > 0 Example: (11, 17, 23) d = 6 Now (p - d)*(p + d) = pa * pb Or: p^2 - d^2 = pa * pb And: p^2 = pa * pb + d^2 Represents a right triangle with: hypotenuse = p leg = d leg = (pa * pb)^0.5 It can be demonstrated that there is no other triplet of primes (pa', p', pb') with d' = p' - pa' = pb' - p' and p ≠ p' such...
Leonel Morales Mar 21
• ### Re: [PrimeNumbers] No Set of 5 Co nsecutive TPM’s Exists such that--

Out of curiosity, how did you find the five TPMs? I am trying to find two pairs of prime pairs (pa, pb) and (pa', pb') all greater than 2, such that: for n = (pb - pa)/2 // pb > pa so n > 0 and equivalent n' calculated in the same way n and n' are integers and d = pb - n = n - pa // d integer, d' calculated in the same way d/n = d'/n' or pa/n = pa'/n' and pb/n = pb'/n' I am...
Leonel Morales Mar 21
• ### Re: [PrimeNumbers] What if Mr. X would have a formula for the prime series?

Wouldn' t it be enough if given prime pn the formula calculates pn+1? All tests for primality would have to be reviewed. Any algorithm depending on primality testing could get a boost in performance from the formula. Cryptography and on line security could be severely affected. Knowing that no prime is missing in the sequence someone could be tempted to create a new encoding system...
Leonel Morales Apr 3, 2013