Prime p₀= 934128967633653551 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 46 2 28 2 28 2 16 2 22 2 (?)
a_n: 0 2 90 92 138 140 168 170 198 200 216 218 240 242
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: 242
Found by: Theadalus
db: batch=76, k=14, 88 46 28 28 16 22

SPT(16)	934128223919376203	0 68 86 170 200 204 224 240 284 300 320 324 354 438 456 524	-743714277348
STPT(10)	934128383738242871	0 2 6 8 48 50 90 92 96 98	-583895410680
SPT(16)	934128414828704983	0 10 28 46 54 66 76 90 94 108 118 130 138 156 174 184	-552804948568
SPT(16)	934128460629996329	0 38 74 90 102 104 144 168 284 308 348 350 362 378 414 452	-507003657222
SPT(16)	934128471154821991	0 6 42 66 70 96 112 126 166 180 196 222 226 250 286 292	-496478831560
STPT(10)	934128658209612959	0 2 30 32 60 62 90 92 120 122	-309424040592
SPT(16)	934129073057713823	0 14 36 50 66 80 96 104 210 218 234 248 264 278 300 314	105424060272
SPT(16)	934129098836578741	0 12 22 40 42 108 126 150 178 202 220 286 288 306 316 328	131202925190
SPT(16)	934129389115066643	0 20 44 56 90 120 140 170 174 204 224 254 288 300 324 344	421481413092
STPT(10)	934129599159376577	0 2 12 14 42 44 72 74 84 86	631525723026
STPT(10)	934129615825268459	0 2 18 20 60 62 102 104 120 122	648191614908