Prime p₀= 927569361820359539 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 40 2 58 2 28 2 40 2 4 2 (?)
a_n: 0 2 108 110 150 152 210 212 240 242 282 284 288 290
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: 290
Found by: crashtech
db: batch=76, k=14, 106 40 58 28 40 4

SPT(16)	927568090962731291	0 30 38 50 62 72 98 108 152 162 188 198 210 222 230 260	-1270857628248
SPT(16)	927568865998261363	0 10 18 64 106 108 120 130 174 184 196 198 240 286 294 304	-495822098176
SPT(16)	927569022432726601	0 36 96 130 186 226 252 256 306 310 336 376 432 466 526 562	-339387632938
STPT(10)	927569211853046141	0 2 36 38 78 80 120 122 156 158	-149967313398
SPT(16)	927569330011975381	0 22 40 106 108 112 120 148 180 208 216 220 222 288 306 328	-31808384158
SPT(16)	927569335094462143	0 28 46 100 108 130 154 180 184 210 234 256 264 318 336 364	-26725897396
SPT(16)	927569505611825597	0 2 30 72 92 120 132 140 156 164 176 204 224 266 294 296	143791466058
TPT(14)	927570399476429699	0 2 42 44 48 50 90 92 132 134 210 212 258 260	1037656070160
STPT(10)	927570740453445227	0 2 60 62 72 74 84 86 144 146	1378633085688
STPT(10)	927570856246440191	0 2 30 32 60 62 90 92 120 122	1494426080652
STPT(10)	927570909369442319	0 2 42 44 60 62 78 80 120 122	1547549082780