Prime p₀= 2214514308798359849 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 40 2 28 2 100 2 4 2 58 2 (?)
a_n: 0 2 108 110 150 152 180 182 282 284 288 290 348 350
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: 350
Found by: ginga
db: batch=81, k=14, 106 40 28 100 4 58

STPT(10)	2214513210429479171	0 2 36 38 78 80 120 122 156 158	-1098368880678
SPT(16)	2214513213220291189	0 12 22 42 48 78 100 120 160 180 202 232 238 258 268 280	-1095578068660
SPT(16)	2214513298859500697	0 6 44 84 116 156 170 182 204 216 230 270 302 342 380 386	-1009938859152
SPT(18)	2214513420631303903	0 16 34 66 114 156 168 180 244 300 364 376 388 430 478 510 528 544	-888167055946
SPT(16)	2214513718378852213	0 4 30 64 100 126 180 196 264 280 334 360 396 430 456 460	-590419507636
STPT(10)	2214514070034597761	0 2 126 128 138 140 150 152 276 278	-238763762088
SPT(16)	2214514405630964473	0 64 66 78 108 124 154 166 168 180 210 226 256 268 270 334	96832604624
STPT(10)	2214514435908004331	0 2 6 8 48 50 90 92 96 98	127109644482
STPT(10)	2214514573521199919	0 2 12 14 30 32 48 50 60 62	264722840070
SPT(16)	2214514591271054927	0 2 12 60 66 110 122 126 140 144 156 200 206 254 264 266	282472695078
SPT(18)	2214514621618100029	0 28 82 114 144 172 238 264 274 348 358 384 450 478 508 540 594 622	312819740180