Prime p₀= 2866420551514891751 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 88 2 16 2 10 2 4 2 (?)
a_n: 0 2 78 80 120 122 210 212 228 230 240 242 246 248
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: 248
Found by: JayPi
db: batch=82, k=14, 76 40 88 16 10 4

SPT(16)	2866419601327047331	0 16 46 70 88 96 118 142 156 180 202 210 228 252 282 298	-950187844420
STPT(10)	2866419622497119231	0 2 6 8 48 50 90 92 96 98	-929017772520
STPT(10)	2866419839355747971	0 2 6 8 18 20 30 32 36 38	-712159143780
STPT(10)	2866419849655470917	0 2 12 14 42 44 72 74 84 86	-701859420834
SPT(16)	2866420094691348329	0 12 54 114 122 128 164 170 222 228 264 270 278 338 380 392	-456823543422
SPT(16)	2866420412129593981	0 6 36 88 90 106 126 156 160 190 210 226 228 280 310 316	-139385297770
SPT(16)	2866420912762811737	0 34 46 60 126 154 156 210 286 340 342 370 436 450 462 496	361247919986
STPT(10)	2866420941715787591	0 2 36 38 78 80 120 122 156 158	390200895840
TPT(14)	2866421021660691179	0 2 60 62 198 200 252 254 282 284 408 410 450 452	470145799428
SPT(16)	2866421023723046183	0 18 84 108 210 228 234 248 276 290 296 314 416 440 506 524	472208154432
SPT(16)	2866421058122187031	0 72 76 82 96 112 142 156 226 240 270 286 300 306 310 382	506607295280