A236071: Primes p such that p^4 - p - 1 is prime.

Sounds noisy like other prime sequences but audibly choppy/crunchy. Not very harmonic either.

Residue counts:
2   [1, 5694]
3   [0, 2879, 2816]
4   [0, 2886, 1, 2808]
5   [1, 1427, 1418, 1465, 1384]
6   [0, 2879, 1, 0, 0, 2815]
7   [1, 1131, 1118, 0, 1161, 1163, 1121]
8   [0, 1401, 1, 1410, 0, 1485, 0, 1398]
9   [0, 931, 933, 0, 952, 953, 0, 996, 930]
10   [0, 1427, 1, 1465, 0, 1, 0, 1417, 0, 1384]
11   [1, 616, 611, 0, 642, 640, 642, 633, 648, 602, 660]
12   [0, 1458, 1, 0, 0, 1428, 0, 1421, 0, 0, 0, 1387]

First 100 first differences:
[3, 2, 4, 2, 10, 30, 8, 10, 8, 58, 2, 54, 36, 10, 12, 42, 24, 56, 60, 90, 76, 2, 82, 44, 132,
18, 10, 24, 80, 18, 154, 66, 68, 6, 126, 52, 2, 306, 12, 70, 128, 12, 76, 120, 6, 8, 46, 30,
36, 6, 8, 70, 30, 144, 26, 90, 126, 10, 168, 246, 14, 88, 14, 34, 122, 10, 32, 42, 4, 20, 36,
24, 42, 28, 12, 54, 78, 90, 2, 76, 164, 154, 60, 24, 68, 54, 100, 318, 2, 204, 76, 44, 66, 30,
64, 24, 180, 72, 8, 90]

The the spectrogram reaveals visible gaps in the sound. This is explained by the large differences
between elements found in the sequence as illustrated by the differences above. Harmonic lines at
7350Hz and 14700Hz corresponding to 44100/3 and 44100/6 respectively. The lines, however, appear
only faintly.

-- Joeph Rafael

This is a quite sparse sequence, with only 5695 terms less than 10^6.

-- Matthew Conroy