missing primes

[AntonioLao]

In a sieve of Diophantus, there are whole numbers that are found in the prime locations and yet they are not primes. However, further investigations have found that most of these composites have only 2 prime factors and most are squarefrees, coprimes, with some primitive prime factors. For those numbers less than 100 are the following: 25, 35, 55, 65, 77, 85, 91, and 95. More detailed investigations allow an assertion that numbers located in the two prime positions at relative group-6 indices G22 and G32 if not themselves primes have prime factors composed of squarefrees, coprimes, primitive prime factors, and integral powers of primes. There are 125 primes between 1 and 700 but 111 non-primes in prime locations. However, the Prime Number Theorem predicted approximately 107 primes between 1 and 700. Even without adding the additive error derived from Riemann zeta function, this number 107 is closer to the non-prime number 111 than to the actual prime number count of 125.

[mkirkpatrick]

Are they really missing?Or just don't exist! That is the question my dear Watson.




regards michael.

[AntonioLao]

They are composites but by their relative sieve positions they all ought to be prime numbers.

[mkirkpatrick]

They are composites but by their relative sieve positions they all ought to be prime numbers.

Then why are they not then?




regards michael.

[AntonioLao]

They are semiprimes which have the potentiality to be primes. This potentiality could also apply to infinity itself. There is a very good chance that infinity is the largest prime.