Prime p₀= 404875917498601001 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 6 20 40 60 20 30 16 30 20 60 40 20 6 (?)
a_n: 0 6 26 66 126 146 176 192 222 242 302 342 362 368
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 368
Found by: Cruncher Pete
db: batch=70, k=14, 6 20 40 60 20 30 16

SPT(14)	404875879419906049	0 78 100 102 112 114 130 162 178 180 190 192 214 292	-38078694952
STPT(10)	404875891564309367	0 2 42 44 72 74 102 104 144 146	-25934291634
SPT(14)	404875893716336827	0 12 22 42 46 64 72 94 102 120 124 144 154 166	-23782264174
SPT(14)	404875899379525801	0 6 16 28 36 42 52 96 106 112 120 132 142 148	-18119075200
SPT(14)	404875909071290389	0 28 64 78 84 94 108 130 144 154 160 174 210 238	-8427310612
SPT(14)	404875914742724881	0 36 40 78 88 102 106 162 166 180 190 228 232 268	-2755876120
SPT(14)	404875919183749789	0 42 70 72 90 118 168 172 222 250 268 270 298 340	1685148788
SPT(14)	404875931026551533	0 30 38 44 98 150 168 260 278 330 384 390 398 428	13527950532
SPT(14)	404875945532706673	0 64 70 88 138 148 160 168 180 190 240 258 264 328	28034105672
TPT(12)	404875988938490297	0 2 60 62 72 74 114 116 174 176 222 224	71439889296
TPT(12)	404876011283227871	0 2 6 8 48 50 60 62 78 80 156 158	93784626870