Prime p₀= 2234740501459756919 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 148 2 10 2 28 2 4 2 22 2 (?)
a_n: 0 2 30 32 180 182 192 194 222 224 228 230 252 254
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: 254
Found by: Penguin
db: batch=81, k=14, 28 148 10 28 4 22

SPT(16)	2234738470054597183	0 10 46 76 108 166 228 250 264 286 348 406 438 468 504 514	-2031405159736
STPT(10)	2234738876422719221	0 2 36 38 78 80 120 122 156 158	-1625037037698
SPT(16)	2234738923012095163	0 28 58 94 108 130 154 166 228 240 264 286 300 336 366 394	-1578447661756
SPT(16)	2234739228577142489	0 2 60 74 102 170 180 210 254 284 294 362 390 404 462 464	-1272882614430
STPT(10)	2234739609911569151	0 2 96 98 138 140 180 182 276 278	-891548187768
SPT(18)	2234739860324867557	0 12 30 54 100 114 180 202 216 280 294 316 382 396 442 466 484 496	-641134889362
SPT(13)	2234740645603098671	0 30 42 48 90 108 120 132 150 192 198 210 240	144143341752
SPT(20)	2234740985869169123	0 14 26 54 78 86 110 120 150 180 194 224 254 264 288 296 320 348 360 374	484409412204
SPT(16)	2234740991863766623	0 4 28 48 76 96 124 150 154 180 208 228 256 276 300 304	490404009704
SPT(16)	2234741362915407461	0 20 36 66 86 92 108 120 218 230 246 252 272 302 318 338	861455650542
STPT(12)	2234742417160485917	0 2 42 44 60 62 84 86 102 104 144 146	1915700728998