bunching up of primes

[Neil Fernandez]

And for the bunching up of primes:

primes for which the x closest primes are smaller:


x=2:
113, 139, 181, 199, 241, 283, 293, 317, 467, 509, 523, 577, 619, 661,
773, 829, 839, 863, 887, 953, 1021, 1039, 1069, 1129, 1237, 1307, 1327,
1381, 1459, 1499, 1583, 1627, 1637, 1669, 1699, 1759, 1789, 1879, 1913,
1951, 2003, 2039, 2089, 2113, 2143, 2221, 2243, 2251, 2273, 2297, 2311,
2357, 2399, 2423, 2447, 2477, 2557, 2593, 2663, 2719, 2753, 2803, 2861,
2971, 3023,...

x=3:
113, 199, 317, 467, 829, 863, 887, 1129, 1307, 1327, 1637, 1669, 1879,
1951, 2089, 2251, 2311, 2477, 2557, 2803, 2971, 3229, 3259, 3271, 3373,
3469, 3739, 3947, 4027, 4139, 4297, 4463, 4523, 4733, 5023, 5119, 5237,
5351, 5449, 5483, 5531, 5591, 5659, 5749, 5881, 6491, 6581, 6841, 6917,
7129, 7253, 7759, 7883, 7963, 8123, 8243, 8297, 8389, 8467, 8543, 8867,
8971, 9013, 9293, 9349, 9439, 9551, 9697, 9749, 9973, 10111, 10273,
10343, 10463


x=4:
113, 1327, 2557, 2803, 2971, 3271, 3469, 4027, 4297, 4523, 5119, 5449,
5531, 5591, 7253, 7883, 8389, 9013, 9439, 9551, 10111, 10909, 11177,
11839, 12119, 12163, 12853, 12923, 13187, 13339, 13729, 13933, 14563,
15683, 15823, 16073, 16141, 16573, 17209, 17989, 18803, 18919, 19087,
19609, 20809, 21031, 21529, 21617, 22307, 22573


x=5:
1327, 3469, 9439, 12119, 13187, 14563, 15683, 15823, 19609, 21031,
21617, 22307, 22573, 23689, 25261, 25471, 29033, 29881, 31277, 31397,
32803, 33647, 34061, 35543, 35617, 38461, 39251, 40289, 40639, 42863,
43331, 43801, 44293, 45139, 47743, 47981, 48497, 48679, 49559, 52391,
55351, 59281

x=6:
1327, 14563, 15683, 19609, 22307, 25471, 31397, 33647, 35617, 39251,
43801, 44293, 49559, 69263, 69499, 76003, 79699, 81569, 82073, 85853,
88681, 88819, 89689, 95819, 102701


x=7:
15683, 25471, 31397, 43801, 44293, 69499, 89689, 102701


x=8:
15683, 31397, 43801, 44293, 89689


and the sequence in which a(n) is the first prime for which n primes are
smaller:

3, 113, 113, 113, 1327, 1327, 15683, 15683

Neil
-- 
Neil Fernandez