Prime p₀= 944686561813087319 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 40 2 28 2 88 2 16 2 22 2 (?)
a_n: 0 2 48 50 90 92 120 122 210 212 228 230 252 254
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: HenkM
db: batch=76, k=14, 46 40 28 88 16 22

SPT(16)	944686189422906839	0 18 24 30 72 80 90 102 110 122 132 140 182 188 194 212	-372390180480
TPT(14)	944686222420059017	0 2 42 44 84 86 120 122 132 134 150 152 162 164	-339393028302
SPT(13)	944686328380885201	0 30 66 96 132 150 216 282 300 336 366 402 432	-233432202118
STPT(10)	944686344840257417	0 2 30 32 72 74 114 116 144 146	-216972829902
SPT(16)	944686392732979439	0 12 54 104 162 174 242 258 314 330 398 410 468 518 560 572	-169080107880
STPT(10)	944686454702267549	0 2 18 20 30 32 42 44 60 62	-107110819770
TPT(14)	944686811957862899	0 2 72 74 102 104 162 164 168 170 210 212 228 230	250144775580
SPT(16)	944686831641043697	0 12 84 122 126 134 164 170 246 252 282 290 294 332 404 416	269827956378
STPT(10)	944687265647118137	0 2 60 62 72 74 84 86 144 146	703834030818
SPT(16)	944687306903879417	0 42 60 62 74 84 90 92 102 104 110 120 132 134 152 194	745090792098
STPT(10)	944687423059873739	0 2 78 80 120 122 162 164 240 242	861246786420