Prime p₀= 2907087557262139649 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 76 2 28 2 22 2 16 2 10 2 (?)
a_n: 0 2 60 62 138 140 168 170 192 194 210 212 222 224
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: 224
Found by: Landjunge
db: batch=82, k=14, 58 76 28 22 16 10

SPT(16)	2907086160331227167	0 12 14 42 80 116 152 236 270 354 390 426 464 492 494 506	-1396930912482
SPT(16)	2907086365719782963	0 6 30 48 80 90 140 168 176 204 254 264 296 314 338 344	-1191542356686
STPT(10)	2907086422653695831	0 2 6 8 48 50 90 92 96 98	-1134608443818
STPT(10)	2907086961416794697	0 2 60 62 102 104 144 146 204 206	-595845344952
STPT(10)	2907086963216259149	0 2 18 20 30 32 42 44 60 62	-594045880500
STPT(10)	2907087497594605067	0 2 12 14 42 44 72 74 84 86	-59667534582
SPT(16)	2907088333354842409	0 42 48 100 132 138 174 178 264 268 304 310 342 394 400 442	776092702760
SPT(16)	2907088360824325193	0 8 14 26 36 54 98 110 204 216 260 278 288 300 306 314	803562185544
STPT(10)	2907088752499188581	0 2 36 38 78 80 120 122 156 158	1195237048932
STPT(10)	2907089290869921257	0 2 90 92 102 104 114 116 204 206	1733607781608
SPT(16)	2907089325015708901	0 18 22 46 48 82 90 120 178 208 216 250 252 276 280 298	1767753569252