Prime p₀= 1235438642439048041 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 22 2 28 2 16 2 28 2 76 2 (?)
a_n: 0 2 96 98 120 122 150 152 168 170 198 200 276 278
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: 278
Found by: Cruncher Pete
db: batch=77, k=14, 94 22 28 16 28 76

SPT(16)	1235437169854507339	0 70 102 154 180 208 214 252 280 318 324 352 378 430 462 532	-1472584540702
SPT(16)	1235437298020289629	0 18 70 100 102 172 174 184 228 238 240 310 312 342 394 412	-1344418758412
SPT(16)	1235437720887199031	0 2 26 42 60 68 116 168 170 222 270 278 296 312 336 338	-921551849010
STPT(10)	1235437992395156447	0 2 60 62 72 74 84 86 144 146	-650043891594
SPT(16)	1235438117798350777	0 24 42 70 94 124 142 154 180 192 210 240 264 292 310 334	-524640697264
STPT(10)	1235438542417498817	0 2 30 32 72 74 114 116 144 146	-100021549224
STPT(10)	1235438989420256981	0 2 6 8 48 50 90 92 96 98	346981208940
STPT(10)	1235439015720112937	0 2 30 32 42 44 54 56 84 86	373281064896
TPT(14)	1235439260301715409	0 2 12 14 42 44 48 50 108 110 150 152 222 224	617862667368
SPT(16)	1235439445344791893	0 6 30 48 78 96 118 126 148 156 178 196 226 244 268 274	802905743852
SPT(16)	1235439451970630741	0 2 6 8 42 50 92 120 128 156 198 206 240 242 246 248	809531582700