A023200: Primes p such that p + 4 is also prime.

Very crackly and consistently noisy throughout.

Residue counts:
2   [0, 8144]
3   [1, 8143, 0]
4   [0, 4003, 0, 4141]
5   [0, 0, 2759, 2683, 2702]
6   [0, 8143, 0, 1, 0, 0]
7   [1, 1615, 1648, 1, 1636, 1595, 1648]
8   [0, 1963, 0, 2074, 0, 2040, 0, 2067]
9   [0, 2682, 0, 1, 2692, 0, 0, 2769, 0]
10   [0, 0, 0, 2683, 0, 0, 0, 2759, 0, 2702]
11   [0, 904, 916, 922, 895, 896, 929, 1, 911, 880, 890]
12   [0, 4003, 0, 1, 0, 0, 0, 4140, 0, 0, 0, 0]

Density information:
A(x) at x=10,100,1000,...:
[2, 9, 41, 203, 1216, 8144]

A(x)/x at x=10,100,1000,...:
0.2,0.09,0.041,0.0203,0.01216,0.008144,

First 100 first differences:
[4, 6, 6, 18, 6, 24, 12, 18, 6, 6, 18, 36, 30, 30, 6, 48, 30, 6, 36, 30,
 18, 42, 18, 6, 24, 12, 114, 30, 30, 66, 18, 12, 54, 30, 6, 18, 6, 24, 30, 
 30, 42, 78, 6, 120, 66, 18, 6, 120, 6, 18, 36, 6, 60, 18, 12, 18, 12, 54, 30, 
 90, 84, 6, 120, 6, 84, 54, 66, 36, 30, 24, 54, 30, 12, 48, 36, 66, 78, 42, 24, 
 6, 18, 42, 48, 36, 24, 96, 66, 18, 42, 84, 24, 30, 36, 66, 24, 114, 6, 66, 84, 60]

First 99 second differences:
[2,0,12,-12,18,-12,6,-12,0,12,18,-6,0,-24,42,-18,-24,30,-6,-12,24,-24,-12,18,-12,
 102,-84,0,36,-48,-6,42,-24,-24,12,-12,18,6,0,12,36,-72,114,-54,-48,-12,114,-114,
 12,18,-30,54,-42,-6,6,-6,42,-24,60,-6,-78,114,-114,78,-30,12,-30,-6,-6,30,-24,
 -18,36,-12,30,12,-36,-18,-18,12,24,6,-12,-12,72,-30,-48,24,42,-60,6,6,30,-42,90,
 -108,60,18,-24]

Distinct line at 7350Hz corresponding to 44100/6. We can observe that this sequence
will not contain any primes that are congruent to 5 mod 6 because for any primes
of the form 6n-1 it will not hold true that 6n+3 is prime as it is divisible by 3.


-- David Oh