Prime p₀= 1023124268797780139 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 10 2 76 2 28 2 10 2 58 2 (?)
a_n: 0 2 90 92 102 104 180 182 210 212 222 224 282 284
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: 284
Found by: stoneageman
db: batch=76, k=14, 88 10 76 28 10 58

SPT(16)	1023123294260757223	0 4 30 48 84 100 120 130 144 154 174 190 226 244 270 274	-974537022916
SPT(16)	1023123473530125833	0 20 24 48 56 78 98 108 206 216 236 258 266 290 294 314	-795267654306
STPT(10)	1023123595771733549	0 2 30 32 60 62 90 92 120 122	-673026046590
SPT(20)	1023123633019864141	0 6 10 30 58 72 82 126 132 178 240 286 292 336 346 360 388 408 412 418	-635777915998
SPT(16)	1023124000331880977	0 6 36 132 230 236 246 252 314 320 330 336 434 530 560 566	-268465899162
STPT(10)	1023124106130947867	0 2 54 56 72 74 90 92 144 146	-162666832272
STPT(10)	1023124691958670661	0 2 6 8 48 50 90 92 96 98	423160890522
TPT(14)	1023124699383781739	0 2 42 44 120 122 132 134 138 140 192 194 222 224	430586001600
SPT(16)	1023125395981812829	0 12 18 54 58 60 70 84 88 102 112 114 118 154 160 172	1127184032690
STPT(10)	1023125472772665011	0 2 36 38 78 80 120 122 156 158	1203974884872
SPT(16)	1023125635176352439	0 8 32 162 168 242 260 278 294 312 330 404 410 540 564 572	1366378572300