Prime p₀= 2400797685384021071 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 82 2 88 2 64 2 10 2 16 2 (?)
a_n: 0 2 36 38 120 122 210 212 276 278 288 290 306 308
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: 308
Found by: JayPi
db: batch=82, k=14, 34 82 88 64 10 16

SPT(16)	2400796532983355477	0 6 32 66 80 146 174 180 236 242 270 336 350 384 410 416	-1152400665594
STPT(10)	2400796611500538071	0 2 6 8 18 20 30 32 36 38	-1073883483000
SPT(16)	2400796689930464281	0 10 82 102 166 198 222 228 400 406 430 462 526 546 618 628	-995453556790
STPT(10)	2400796838551581851	0 2 78 80 108 110 138 140 216 218	-846832439220
STPT(10)	2400797199574363901	0 2 36 38 108 110 180 182 216 218	-485809657170
TPT(14)	2400797647265704151	0 2 78 80 90 92 168 170 180 182 318 320 330 332	-38118316920
STPT(10)	2400798024585287627	0 2 24 26 42 44 60 62 84 86	339201266556
STPT(10)	2400798050473316411	0 2 30 32 78 80 126 128 156 158	365089295340
SPT(16)	2400798284175285457	0 22 30 60 82 100 106 184 192 270 276 294 316 346 354 376	598791264386
SPT(16)	2400798487469494751	0 42 56 62 86 92 132 140 192 200 240 246 270 276 290 332	802085473680
TPT(14)	2400798766006409927	0 2 30 32 72 74 90 92 144 146 240 242 264 266	1080622388856