Hi,
Here is the prime number distribution for multiples of 3600
the count of primes for a+3600n for n=0 to n=3599
for the first 140 or so values for a (cropped for space)
I found the pattern! :D
if the formula with a produces more than a single prime, then a is ALWAYS either a prime or a product of primes, before I thought it could be a power of primes, but it is actually a product of primes.
ie for a = 17 below the formula is"
17+3600n for n=0 to n=3599and at the range of the first 10million primes I tested to, this formula produced 690 primes.
The reason I call this a generalized formula, is because a is always a prime or a product of primes, and the 3600 is arbitrary as long as it is a multiple of 6 I think.
cheers, Jamie
a, count
{[0, 0]} {[1, 690]} {[2, 1]} {[3, 1]} {[4, 0]} {[5, 1]} {[6, 0]} {[7, 698]} {[8, 0]} {[9, 0]} {[10, 0]} {[11, 687]} {[12, 0]} {[13, 694]} {[14, 0]} {[15, 0]} {[16, 0]} {[17, 690]} {[18, 0]} {[19, 691]} {[20, 0]} {[21, 0]} {[22, 0]} {[23, 697]} {[24, 0]} {[25, 0]} {[26, 0]} {[27, 0]} {[28, 0]} {[29, 672]} {[30, 0]} {[31, 689]} {[32, 0]} {[33, 0]} {[34, 0]} {[35, 0]} {[36, 0]} {[37, 712]} {[38, 0]} {[39, 0]} {[40, 0]} {[41, 688]} {[42, 0]} {[43, 684]} {[44, 0]} {[45, 0]} {[46, 0]} {[47, 702]} {[48, 0]} {[49, 688]} {[50, 0]} {[51, 0]} {[52, 0]} {[53, 677]} {[54, 0]} {[55, 0]} {[56, 0]} {[57, 0]} {[58, 0]} {[59, 669]} {[60, 0]} {[61, 678]} {[62, 0]} {[63, 0]} {[64, 0]} {[65, 0]} {[66, 0]} {[67, 686]} {[68, 0]} {[69, 0]} {[70, 0]} {[71, 698]} {[72, 0]} {[73, 671]} {[74, 0]} {[75, 0]} {[76, 0]} {[77, 691]} {[78, 0]} {[79, 693]} {[80, 0]} {[81, 0]} {[82, 0]} {[83, 711]} {[84, 0]} {[85, 0]} {[86, 0]} {[87, 0]} {[88, 0]} {[89, 685]} {[90, 0]} {[91, 700]} {[92, 0]} {[93, 0]} {[94, 0]} {[95, 0]} {[96, 0]} {[97, 696]} {[98, 0]} {[99, 0]} {[100, 0]} {[101, 710]} {[102, 0]} {[103, 682]} {[104, 0]} {[105, 0]} {[106, 0]} {[107, 691]} {[108, 0]} {[109, 680]} {[110, 0]} {[111, 0]} {[112, 0]} {[113, 690]} {[114, 0]} {[115, 0]} {[116, 0]} {[117, 0]} {[118, 0]} {[119, 688]} {[120, 0]} {[121, 683]} {[122, 0]} {[123, 0]} {[124, 0]} {[125, 0]} {[126, 0]} {[127, 730]} {[128, 0]} {[129, 0]} {[130, 0]} {[131, 689]} {[132, 0]} {[133, 692]} {[134, 0]} {[135, 0]} {[136, 0]} {[137, 694]} {[138, 0]} {[139, 688]} {[140, 0]} {[141, 0]}
... continues to 3599