Prime p₀= 2732257716610237631 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 46 2 16 2 52 2 58 2 (?)
a_n: 0 2 60 62 90 92 138 140 156 158 210 212 270 272
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: 272
Found by: JayPi
db: batch=82, k=14, 58 28 46 16 52 58

TPT(14)	2732256559444445699	0 2 42 44 78 80 240 242 330 332 360 362 402 404	-1157165791932
STPT(10)	2732256575733783347	0 2 30 32 42 44 54 56 84 86	-1140876454284
TPT(14)	2732256740998029431	0 2 30 32 60 62 90 92 156 158 168 170 240 242	-975612208200
SPT(16)	2732257126783263841	0 40 76 90 100 138 166 220 258 312 340 378 388 402 438 478	-589826973790
SPT(16)	2732257130714311201	0 18 40 42 130 150 166 310 348 492 508 528 616 618 640 658	-585895926430
SPT(16)	2732257346194531291	0 16 96 120 138 148 196 198 208 210 258 268 286 310 390 406	-370415706340
STPT(10)	2732257724254460837	0 2 30 32 42 44 54 56 84 86	7644223206
SPT(16)	2732258293535586163	0 40 46 60 78 96 106 108 148 150 160 178 196 210 216 256	576925348532
SPT(16)	2732258443798830433	0 4 60 64 76 154 160 166 168 174 180 258 270 274 330 334	727188592802
SPT(16)	2732258628158202163	0 4 28 30 70 118 130 138 160 168 180 228 268 270 294 298	911547964532
TPT(14)	2732258629348476269	0 2 72 74 150 152 198 200 240 242 252 254 312 314	912738238638