Prime p₀= 2316488583222093821 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 70 2 88 2 16 2 70 2 10 2 (?)
a_n: 0 2 6 8 78 80 168 170 186 188 258 260 270 272
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: 272
Found by: Orange Kid
db: batch=81, k=14, 4 70 88 16 70 10

SPT(16)	2316487688056095457	0 16 30 70 72 126 150 154 252 256 280 334 336 376 390 406	-895165998364
STPT(10)	2316487808078997587	0 2 60 62 72 74 84 86 144 146	-775143096234
SPT(16)	2316488012378999717	0 12 32 102 126 146 230 264 272 306 390 410 434 504 524 536	-570843094104
SPT(16)	2316488195131088401	0 16 30 36 66 70 78 100 168 190 198 202 232 238 252 268	-388091005420
STPT(10)	2316488209547175437	0 2 42 44 72 74 102 104 144 146	-373674918384
SPT(16)	2316488255598008287	0 6 12 24 34 52 82 90 196 204 234 252 262 274 280 286	-327624085534
SPT(16)	2316488883513477151	0 40 48 90 96 118 136 156 160 180 198 220 226 268 276 316	300291383330
STPT(10)	2316488943441816641	0 2 36 38 78 80 120 122 156 158	360219722820
STPT(10)	2316489410050956191	0 2 6 8 18 20 30 32 36 38	826828862370
SPT(16)	2316489584478297923	0 38 80 84 114 126 144 158 216 230 248 260 290 294 336 374	1001256204102
TPT(14)	2316490492280872967	0 2 42 44 90 92 120 122 174 176 222 224 234 236	1909058779146