IIRC, one of the great mathematical goals is a Prime Number Generator.
(you do know what a prime number IS…don’t you?)
in this thread:
I (re)discovered the general form of prime numbers: except for 2 and 3, all primes are of the form (6*X)+or- 1.
What is X?
Running this simple formula in my head, and later on paper, I figured X must itself be prime.
If we designate 1,2, and 3 as quasi-prime (not true primes as they are NOT of the form (6*X)+ or- 1), then this formula does indeed start generating new primes:
COLUMN 1 COLUMN 2
(61)+/-1= 5 and 7
(62)+/-1= 11 and 13
(63)+/-1= 17 and 19 (64)+/-1= 23, not 25
(65)+/-1= 29 and 31 (66)+/-1= 37, not 35
(67)+/-1= 41 and 43 (68)+/-1= 47, not 49
(69)+/-1= 53, not 55 (610)+/-1=59 and 61
AFAIK, when X is prime, the formula does indeed generate a new prime(col1), yet some primes are generated by the formula when X is NOT prime.
Yes, these are both pretty trivial rules, and there are a million like them: 4x plus or minus 1 (except for 2) because otherwise you’d be divisible by 2. 6x plus or minus 1 (except for 2 and 3) because otherwise you’d be divisible by 2 or divisible by 3. 10x plus or minus 1 or 3 (except for 2 and 5) because otherwise you’d be divisible by 2 or divisible by 5. These things are a dime a dozen, I’m afraid.
Yes. The very next case: 6 * 11 - 1 = 65, which isn’t prime, even though 11 is prime. For an example using plus instead of minus, 6 * 19 + 1 = 115, which, again, isn’t prime, even though 19 is.
