Prime p₀= 1142323124371243271 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 136 2 10 2 28 2 124 2 10 2 (?)
a_n: 0 2 90 92 228 230 240 242 270 272 396 398 408 410
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: 410
Found by: Theadalus
db: batch=76, k=14, 88 136 10 28 124 10

SPT(16)	1142321735187334453	0 24 34 70 94 100 118 126 148 156 174 180 204 240 250 274	-1389183908818
STPT(10)	1142322026502896891	0 2 36 38 78 80 120 122 156 158	-1097868346380
SPT(16)	1142322187420003649	0 12 50 54 68 78 92 134 168 210 224 234 248 252 290 302	-936951239622
STPT(10)	1142322579225111041	0 2 6 8 18 20 30 32 36 38	-545146132230
STPT(10)	1142323013783985791	0 2 6 8 18 20 30 32 36 38	-110587257480
SPT(16)	1142323026544287781	0 30 46 90 96 198 216 228 238 250 268 370 376 420 436 466	-97826955490
STPT(10)	1142323694594679557	0 2 30 32 102 104 174 176 204 206	570223436286
STPT(10)	1142323811198267051	0 2 6 8 48 50 90 92 96 98	686827023780
SPT(16)	1142324086226742511	0 22 82 108 112 138 148 166 222 240 250 276 280 306 366 388	961855499240
SPT(16)	1142324113624247971	0 40 60 88 106 130 132 156 172 196 198 222 240 268 288 328	989253004700
STPT(10)	1142324144204951801	0 2 36 38 78 80 120 122 156 158	1019833708530