Prime p₀= 2048719844755069427 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 10 2 4 2 40 2 40 2 (?)
a_n: 0 2 12 14 42 44 54 56 60 62 102 104 144 146
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: 146
Found by: Josemi
db: batch=80, k=14, 10 28 10 4 40 40

SPT(16)	2048717790211446127	0 4 34 54 60 82 96 126 130 160 174 196 202 222 252 256	-2054543623300
SPT(16)	2048718339214022257	0 40 42 46 90 94 112 124 132 144 162 166 210 214 216 256	-1505541047170
SPT(16)	2048718840350428007	0 6 42 62 80 84 192 194 222 224 332 336 354 374 410 416	-1004404641420
SPT(16)	2048719022447863897	0 54 66 70 82 94 124 126 130 132 162 174 186 190 202 256	-822307205530
SPT(16)	2048719365158229073	0 6 10 24 30 70 144 150 154 160 234 274 280 294 298 304	-479596840354
STPT(10)	2048719548571819967	0 2 30 32 42 44 54 56 84 86	-296183249460
SPT(16)	2048720134635961447	0 16 34 94 150 156 204 246 280 322 370 376 432 492 510 526	289880892020
STPT(10)	2048720202178587239	0 2 78 80 120 122 162 164 240 242	357423517812
STPT(10)	2048720408924728727	0 2 24 26 42 44 60 62 84 86	564169659300
TPT(14)	2048720435731987007	0 2 84 86 132 134 174 176 210 212 300 302 312 314	590976917580
TPT(14)	2048720502701118971	0 2 6 8 126 128 180 182 228 230 240 242 258 260	657946049544