Prime p₀= 2121312424694751017 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 142 2 16 2 10 2 34 2 40 2 40 2 (?)
a_n: 0 2 144 146 162 164 174 176 210 212 252 254 294 296
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: Landjunge
db: batch=80, k=14, 142 16 10 34 40 40

SPT(16)	2121311806865432087	0 14 20 44 62 84 96 152 174 230 242 264 282 306 312 326	-617829318930
STPT(10)	2121311927239395599	0 2 18 20 60 62 102 104 120 122	-497455355418
SPT(16)	2121312185390057893	0 34 48 78 114 126 136 150 154 168 178 190 226 256 270 304	-239304693124
STPT(10)	2121312241840820261	0 2 36 38 78 80 120 122 156 158	-182853930756
SPT(16)	2121312302802888031	0 18 28 72 90 96 148 160 168 180 232 238 256 300 310 328	-121891862986
TPT(14)	2121312402994245581	0 2 66 68 108 110 150 152 156 158 288 290 306 308	-21700505436
TPT(14)	2121312707114816429	0 2 12 14 30 32 132 134 222 224 240 242 258 260	282420065412
SPT(16)	2121312886307091193	0 30 66 90 114 126 136 156 178 198 208 220 244 268 304 334	461612340176
TPT(14)	2121312912428846621	0 2 36 38 60 62 210 212 216 218 246 248 258 260	487734095604
SPT(16)	2121312970002838091	0 2 20 30 36 60 162 176 252 266 368 392 398 408 426 428	545308087074
SPT(16)	2121313533165683693	0 30 50 56 74 78 110 114 140 144 176 180 198 204 224 254	1108470932676