Prime p₀= 1236572720367694667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 34 2 10 2 10 2 16 2 10 2 (?)
a_n: 0 2 24 26 60 62 72 74 84 86 102 104 114 116
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: 116
Found by: Spectrum
db: batch=77, k=14, 22 34 10 10 16 10

SPT(16)	1236572131665000821	0 32 38 60 62 80 96 108 140 152 168 186 188 210 216 248	-588702693846
SPT(16)	1236572234250222167	0 42 50 62 86 90 96 146 210 260 266 270 294 306 314 356	-486117472500
SPT(16)	1236572298179156359	0 24 42 78 150 168 204 210 232 238 274 292 364 400 418 442	-422188538308
SPT(16)	1236572338284624127	0 12 30 36 114 180 210 216 330 336 366 432 510 516 534 546	-382083070540
SPT(16)	1236572338928333221	0 6 48 90 100 156 162 178 180 196 202 258 268 310 352 358	-381439361446
STPT(10)	1236572596898871497	0 2 42 44 72 74 102 104 144 146	-123468823170
STPT(10)	1236572963283225479	0 2 18 20 30 32 42 44 60 62	242915530812
SPT(16)	1236573204315637261	0 6 78 142 156 166 168 190 258 280 282 292 306 370 442 448	483947942594
TPT(14)	1236573824579305319	0 2 18 20 120 122 132 134 240 242 288 290 330 332	1104211610652
SPT(16)	1236573927556826149	0 40 82 208 232 238 250 264 298 312 324 330 354 480 522 562	1207189131482
SPT(16)	1236574071436601059	0 12 22 28 42 84 88 114 238 264 268 310 324 330 340 352	1351068906392