bcavnaugh
I thought all of yours were 23
AP20: 120452772347965093+10372758*23#*n for n=0..19 (2016-11-19 07:38:42 UTC)
I wish. I think it's the n=0..19 that makes it a 20.
Below is a 22, notice the n=0..21.
AP22:
277244543103675281+3728817*23#*n for n=0..21 (2016-09-29 09:19:49 UTC)
I think that means this one formula yields 22 prime numbers. Every n 0 through 21 will yield a prime number.
277244543103675281+3728817*23#*0 - is prime
277244543103675281+3728817*23#*1 - is prime
277244543103675281+3728817*23#*2 - is prime
...
277244543103675281+3728817*23#*21 - is prime
That is why it is so much harder to find an AP23, AP24, etc. The whole series has to be true. I may have read the math wrong though...
Edit: thinking about this, it must be more complicated, because it appears way to easy to get an even number using my logic. Oh well, way to early for this thinking...
Edit 2: Couldn't stop researching...
Arithmetic progressions
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.
An arithmetic progression of primes is a sequence of primes with a common difference between any two successive numbers in the sequence. For example 3, 7, 11 is an arithmetic progression of 3 primes with a common difference of 4.
For an arithmetic progression (AP) of primes, AP-k is k primes of the form p + d*n for some d (the common difference between the primes) and k consecutive values of n. The above AP-3 is 3 + 4*n for n=0,1,2.