Prime p₀= 1124891873556085487 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 136 2 58 2 10 2 16 2 22 2 (?)
a_n: 0 2 12 14 150 152 210 212 222 224 240 242 264 266
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: 266
Found by: crashtech
db: batch=76, k=14, 10 136 58 10 16 22

STPT(10)	1124890625207025461	0 2 36 38 78 80 120 122 156 158	-1248349060026
STPT(10)	1124890661312279747	0 2 30 32 72 74 114 116 144 146	-1212243805740
SPT(16)	1124890771437555593	0 6 20 66 80 104 116 128 186 198 210 234 248 294 308 314	-1102118529894
SPT(16)	1124891485605293039	0 18 32 54 74 104 132 174 188 230 258 288 308 330 344 362	-387950792448
STPT(10)	1124891754028152137	0 2 24 26 42 44 60 62 84 86	-119527933350
SPT(16)	1124891867568537293	0 24 30 96 150 156 168 194 240 266 278 284 338 404 410 434	-5987548194
SPT(20)	1124891919285731719	0 24 114 150 192 220 264 280 304 352 360 408 432 448 492 520 562 598 688 712	45729646232
STPT(10)	1124892166783996319	0 2 18 20 60 62 102 104 120 122	293227910832
SPT(16)	1124893026274516067	0 6 24 30 50 56 84 90 116 122 150 156 176 182 200 206	1152718430580
STPT(10)	1124893107597257261	0 2 6 8 48 50 90 92 96 98	1234041171774
TPT(14)	1124893531642645691	0 2 36 38 180 182 216 218 300 302 456 458 486 488	1658086560204