Prime p₀= 1235316930603242777 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 76 2 52 2 58 2 106 2 (?)
a_n: 0 2 12 14 42 44 120 122 174 176 234 236 342 344
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: 344
Found by: Cruncher Pete
db: batch=77, k=14, 10 28 76 52 58 106

SPT(16)	1235315544171562409	0 14 62 80 90 122 132 182 240 290 300 332 342 360 408 422	-1386431680368
STPT(10)	1235316015965432411	0 2 6 8 48 50 90 92 96 98	-914637810366
SPT(16)	1235316079650878441	0 6 42 56 60 80 98 116 132 150 168 188 192 206 242 248	-850952364336
SPT(16)	1235316482354333459	0 38 72 78 80 92 108 132 170 194 210 222 224 230 264 302	-448248909318
TPT(14)	1235316494068090667	0 2 72 74 120 122 210 212 270 272 294 296 330 332	-436535152110
SPT(16)	1235316802798718851	0 28 58 70 78 96 142 178 210 246 292 310 318 330 360 388	-127804523926
STPT(10)	1235316934166024189	0 2 18 20 30 32 42 44 60 62	3562781412
SPT(16)	1235316968100532363	0 4 34 54 144 156 166 208 246 288 298 310 400 420 450 454	37497289586
STPT(10)	1235317083809902967	0 2 30 32 42 44 54 56 84 86	153206660190
SPT(13)	1235317129072587563	0 6 30 90 114 144 150 156 186 210 270 294 300	198469344786
STPT(10)	1235317147098837989	0 2 18 20 30 32 42 44 60 62	216495595212