Prime p₀= 1028528872814716211 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 46 2 16 2 82 2 16 2 40 2 (?)
a_n: 0 2 30 32 78 80 96 98 180 182 198 200 240 242
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: GLeeM
db: batch=76, k=14, 28 46 16 82 16 40

SPT(16)	1028527912789699583	0 30 56 74 104 114 204 216 284 296 386 396 426 444 470 500	-960025016628
STPT(10)	1028528071839788489	0 2 12 14 30 32 48 50 60 62	-800974927722
STPT(10)	1028528190215567927	0 2 54 56 72 74 90 92 144 146	-682599148284
STPT(10)	1028528475004902041	0 2 30 32 78 80 126 128 156 158	-397809814170
SPT(16)	1028528589319315067	0 20 42 60 62 74 126 170 216 260 312 324 326 344 366 386	-283495401144
SPT(16)	1028528812471692787	0 6 34 36 94 112 126 136 180 190 204 222 280 282 310 316	-60343023424
STPT(10)	1028529347199043577	0 2 30 32 42 44 54 56 84 86	474384327366
STPT(10)	1028530356146780087	0 2 30 32 42 44 54 56 84 86	1483332063876
SPT(16)	1028530710354239509	0 28 54 84 88 114 124 148 180 204 214 240 244 274 300 328	1837539523298
SPT(16)	1028530838233816157	0 84 86 122 144 146 164 174 182 192 210 212 234 270 272 356	1965419099946
STPT(10)	1028530851128690837	0 2 30 32 72 74 114 116 144 146	1978313974626