Prime p₀= 1127314321610730359 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 4 2 40 2 16 2 52 2 4 2 (?)
a_n: 0 2 72 74 78 80 120 122 138 140 192 194 198 200
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: 200
Found by: crashtech
db: batch=76, k=14, 70 4 40 16 52 4

SPT(16)	1127311774586032073	0 8 36 54 96 98 128 164 210 246 276 278 320 338 366 374	-2547024698286
STPT(10)	1127311789319362991	0 2 36 38 78 80 120 122 156 158	-2532291367368
SPT(16)	1127311969479599011	0 6 10 76 78 96 118 120 166 168 190 208 210 276 280 286	-2352131131348
SPT(16)	1127312438197219349	0 8 38 60 62 78 84 104 138 158 164 180 182 204 234 242	-1883413511010
SPT(16)	1127312556390035293	0 54 64 108 120 154 208 238 270 300 354 388 400 444 454 508	-1765220695066
STPT(10)	1127313548258872061	0 2 6 8 48 50 90 92 96 98	-773351858298
SPT(16)	1127314735318074343	0 6 18 28 36 40 130 264 280 414 504 508 516 526 538 544	413707343984
STPT(10)	1127314833383156711	0 2 66 68 138 140 210 212 276 278	511772426352
SPT(16)	1127314979870038871	0 20 42 132 140 162 168 198 260 290 296 318 326 416 438 458	658259308512
TPT(14)	1127315122269209219	0 2 12 14 78 80 90 92 108 110 162 164 342 344	800658478860
SPT(16)	1127315346297614281	0 10 52 66 82 100 112 120 322 330 342 360 376 390 432 442	1024686883922