Prime p₀= 1122586689721242059 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 34 2 88 2 52 2 94 2 28 2 (?)
a_n: 0 2 72 74 108 110 198 200 252 254 348 350 378 380
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: 380
Found by: stoneageman
db: batch=76, k=14, 70 34 88 52 94 28

SPT(16)	1122585315628165439	0 72 78 84 110 114 122 180 182 240 248 252 278 284 290 362	-1374093076620
SPT(16)	1122585736431402413	0 8 30 56 60 66 84 134 150 200 218 224 228 254 276 284	-953289839646
SPT(16)	1122585870142030727	0 6 24 26 42 56 86 116 180 210 240 254 270 272 290 296	-819579211332
STPT(10)	1122585911140611887	0 2 12 14 72 74 132 134 144 146	-778580630172
SPT(16)	1122586201369220933	0 14 36 66 126 140 146 174 200 228 234 248 308 338 360 374	-488352021126
SPT(16)	1122586615705148441	0 26 50 72 102 110 116 162 176 222 228 236 266 288 312 338	-74016093618
TPT(16)	1122586693621193741	0 2 66 68 120 122 180 182 288 290 306 308 330 332 348 350	3899951682
TPT(14)	1122586840617769949	0 2 48 50 78 80 90 92 120 122 168 170 198 200	150896527890
STPT(12)	1122586840617769949	0 2 48 50 78 80 90 92 120 122 168 170	150896527890
SPT(16)	1122586892174903707	0 6 40 60 70 90 96 180 250 334 340 360 370 390 424 430	202453661648
SPT(16)	1122587077393212601	0 10 70 102 132 136 150 178 210 238 252 256 286 318 378 388	387671970542