Prime p₀= 2048312358813937001 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 58 2 4 2 40 2 28 2 (?)
a_n: 0 2 30 32 60 62 120 122 126 128 168 170 198 200
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: 200
Found by: JonS
db: batch=80, k=14, 28 28 58 4 40 28

SPT(16)	2048310542623988369	0 62 102 168 180 228 320 348 452 480 572 620 632 698 738 800	-1816189948632
SPT(18)	2048310630995822729	0 30 44 50 84 92 98 120 128 144 152 174 180 188 222 228 242 272	-1727818114272
STPT(10)	2048311428462743399	0 2 48 50 90 92 132 134 180 182	-930351193602
STPT(10)	2048312034202801397	0 2 30 32 60 62 90 92 120 122	-324611135604
STPT(10)	2048312191952417717	0 2 42 44 72 74 102 104 144 146	-166861519284
SPT(16)	2048312334077616521	0 50 80 96 150 206 248 288 308 348 390 446 500 516 546 596	-24736320480
SPT(16)	2048312899217239513	0 18 36 40 48 60 78 106 108 136 154 166 174 178 196 214	540403302512
TPT(14)	2048313207160341731	0 2 156 158 210 212 288 290 318 320 348 350 390 392	848346404730
SPT(16)	2048313493923121193	0 20 30 44 80 98 156 174 230 248 306 324 360 374 384 404	1135109184192
SPT(16)	2048313836807244289	0 24 34 70 90 108 132 142 150 160 184 202 222 258 268 292	1477993307288
STPT(10)	2048314205400196301	0 2 96 98 168 170 240 242 336 338	1846586259300