Prime p₀= 1526972096319577967 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 40 2 34 2 40 2 70 2 88 2 (?)
a_n: 0 2 12 14 54 56 90 92 132 134 204 206 294 296
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: 296
Found by: crashtech
db: batch=78, k=14, 10 40 34 40 70 88

SPT(16)	1526971322591001163	0 10 34 64 66 84 106 148 156 198 220 238 240 270 294 304	-773728576804
STPT(10)	1526971428118454567	0 2 30 32 42 44 54 56 84 86	-668201123400
STPT(10)	1526971521032703971	0 2 36 38 78 80 120 122 156 158	-575286873996
SPT(16)	1526971684565227787	0 6 84 132 146 150 176 200 276 300 326 330 344 392 470 476	-411754350180
SPT(16)	1526971733481037891	0 22 28 36 48 82 112 126 202 216 246 280 292 300 306 328	-362838540076
STPT(10)	1526972059125735137	0 2 24 26 42 44 60 62 84 86	-37193842830
STPT(10)	1526973066477099251	0 2 90 92 108 110 126 128 216 218	970157521284
SPT(16)	1526973408165088249	0 28 58 60 108 112 142 178 234 270 300 304 352 354 384 412	1311845510282
SPT(16)	1526974529857787719	0 24 34 60 70 100 102 112 132 142 144 174 184 210 220 244	2433538209752
SPT(16)	1526974642181795449	0 24 42 52 82 88 108 118 144 154 174 180 210 220 238 262	2545862217482
STPT(10)	1526975446418799371	0 2 36 38 78 80 120 122 156 158	3350099221404