Prime p₀= 1286357303632744667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 58 2 40 2 10 2 64 2 (?)
a_n: 0 2 30 32 60 62 120 122 162 164 174 176 240 242
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: 242
Found by: Theadalus
db: batch=77, k=14, 28 28 58 40 10 64

SPT(16)	1286355762433436363	0 18 30 78 110 116 126 140 174 188 198 204 236 284 296 314	-1541199308304
SPT(16)	1286355983286126691	0 12 42 70 108 136 148 162 196 210 222 250 288 316 346 358	-1320346617976
SPT(16)	1286356373497748251	0 28 52 66 72 90 96 100 108 112 118 136 142 156 180 208	-930134996416
TPT(14)	1286356441849508801	0 2 186 188 258 260 330 332 336 338 426 428 468 470	-861783235866
STPT(10)	1286357038428829721	0 2 6 8 48 50 90 92 96 98	-265203914946
SPT(16)	1286357127422342683	0 36 58 88 100 120 186 270 316 400 466 486 498 528 550 586	-176210401984
STPT(12)	1286357344406832107	0 2 12 14 42 44 60 62 90 92 102 104	40774087440
STPT(10)	1286357375752354067	0 2 30 32 42 44 54 56 84 86	72119609400
STPT(10)	1286357545511768501	0 2 30 32 78 80 126 128 156 158	241879023834
SPT(16)	1286357635576771403	0 24 38 44 50 104 126 176 198 248 270 324 330 336 350 374	331944026736
SPT(16)	1286358537161147507	0 26 32 54 74 92 102 116 120 134 144 162 182 204 210 236	1233528402840