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Proof of infinite prime numbers

# Proof of infinite prime numbers

## Prime numbers; a visual aid

In order to find the prime numbers from a certain number (9) to twice that same number (2*9 = 18) we only need the prime numbers from 2 to 9. Map those primes on the vertical and the number sequence on the horizontal. Mark every multiple of the listed primes (for 2 that's 2 and 2+2 and 2+2+2 etc). When all prime multiples are charted look for marks in every vertical column from 10 to 18. Those columns without any marks are the prime numbers from 10 to 18.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2 3 5 7 → →

## Calculating the amount of primes between N/2 and N

• Let a0 be 1.
• Let a1 be the value of the first prime number (=2).
• Let a2 be the value of the second prime number (=3).
• Let ap be the value of prime number p.
• Let Ai be the amount of numbers identified to be not primes by the isofactor of i's.

A1 = |N/a0*a1|

A2 = |N/a0*a2| - |N/a1*a2|

A3 = |N/a0*a3| - |N/a1*a3| - |N/a2*a3| + |N/a1*a2*a3|

Etcetera, up to Ap.

The amount of primes between N/2 and N equals N-1-A.

If this amount is to be zero (that is after the hypothetical final prime number) then 0 = N-1-A. In this case A = N-1. When the prime numbers become very large, N becomes very large but the a*a-phrase becomes larger faster. The number A will never be large enough to be N-1.