Prime p₀= 4276920473775362321 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 34 2 28 2 22 2 58 2 16 2 (?)
a_n: 0 2 60 62 96 98 126 128 150 152 210 212 228 230
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: 230
Found by: Stony666
db: batch=85, k=14, 58 34 28 22 58 16

SPT(16)	4276919289163063397	0 24 26 44 56 126 162 180 236 254 290 360 372 390 392 416	-1184612298924
STPT(10)	4276919469080456459	0 2 48 50 60 62 72 74 120 122	-1004694905862
SPT(16)	4276920024318683351	0 12 26 32 68 80 110 152 156 198 228 240 276 282 296 308	-449456678970
STPT(12)	4276920268548477929	0 2 30 32 78 80 162 164 210 212 240 242	-205226884392
TPT(14)	4276920268548477929	0 2 30 32 78 80 162 164 210 212 240 242 252 254	-205226884392
SPT(16)	4276920362627403221	0 8 42 152 170 180 198 206 252 260 278 288 306 416 450 458	-111147959100
SPT(16)	4276920987122255011	0 12 18 30 88 96 102 112 156 166 172 180 238 250 256 268	513346892690
SPT(16)	4276921096068841921	0 10 22 28 46 70 72 100 108 136 138 162 180 186 198 208	622293479600
SPT(16)	4276921460161041569	0 38 48 50 80 138 140 180 260 300 302 360 390 392 402 440	986385679248
STPT(10)	4276921552911570749	0 2 18 20 30 32 42 44 60 62	1079136208428
STPT(10)	4276921865294991947	0 2 60 62 72 74 84 86 144 146	1391519629626