Prime p₀= 1124923667951735651 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 76 2 10 2 4 2 22 2 166 2 (?)
a_n: 0 2 60 62 138 140 150 152 156 158 180 182 348 350
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: 350
Found by: crashtech
db: batch=76, k=14, 58 76 10 4 22 166

SPT(16)	1124922850012588021	0 22 28 30 126 136 142 150 238 246 252 262 358 360 366 388	-817939147630
SPT(16)	1124923046734679917	0 40 46 106 130 156 160 190 222 252 256 282 306 366 372 412	-621217055734
STPT(12)	1124923119373760921	0 2 30 32 60 62 126 128 156 158 186 188	-548577974730
SPT(16)	1124923261730431349	0 14 50 60 72 90 110 132 140 162 182 200 212 222 258 272	-406221304302
SPT(16)	1124923314170346659	0 8 14 20 44 62 78 104 108 134 150 168 192 198 204 212	-353781388992
TPT(14)	1124923609429431311	0 2 36 38 66 68 90 92 126 128 216 218 360 362	-58522304340
SPT(16)	1124923812694478471	0 6 26 50 72 90 110 120 182 192 212 230 252 276 296 302	144742742820
SPT(16)	1124923945559647703	0 8 30 66 84 108 158 194 210 246 296 320 338 374 396 404	277607912052
SPT(16)	1124924178930825851	0 12 26 62 86 110 120 132 140 152 162 186 210 246 260 272	510979090200
STPT(10)	1124924218844589347	0 2 30 32 60 62 90 92 120 122	550892853696
STPT(10)	1124924230509134579	0 2 18 20 30 32 42 44 60 62	562557398928