Prime p₀= 1230594439873654439 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 4 2 82 2 4 2 190 2 16 2 (?)
a_n: 0 2 42 44 48 50 132 134 138 140 330 332 348 350
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: Cruncher Pete
db: batch=77, k=14, 40 4 82 4 190 16

SPT(16)	1230593315033394127	0 60 90 100 132 142 180 186 226 232 270 280 312 322 352 412	-1124840260312
STPT(10)	1230593424338479427	0 2 30 32 72 74 114 116 144 146	-1015535175012
STPT(10)	1230593522157475319	0 2 18 20 30 32 42 44 60 62	-917716179120
STPT(10)	1230593926562186279	0 2 42 44 60 62 78 80 120 122	-513311468160
STPT(10)	1230594036331177499	0 2 42 44 60 62 78 80 120 122	-403542476940
STPT(10)	1230594207344527589	0 2 12 14 90 92 168 170 180 182	-232529126850
SPT(16)	1230594498381102919	0 30 42 82 130 162 208 304 408 504 550 582 630 670 682 712	58507448480
SPT(16)	1230594722789456623	0 16 30 36 60 96 130 154 156 180 214 250 274 280 294 310	282915802184
SPT(16)	1230594761142419539	0 10 60 70 88 102 142 150 172 180 220 234 252 262 312 322	321268765100
SPT(16)	1230594896029144549	0 24 60 100 112 180 198 220 282 304 322 390 402 442 478 502	456155490110
SPT(16)	1230594922168113371	0 42 62 90 102 108 116 146 162 192 200 206 218 246 266 308	482294458932