Prime p₀= 1270575318171766301 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 34 2 10 2 76 2 10 2 40 2 (?)
a_n: 0 2 120 122 156 158 168 170 246 248 258 260 300 302
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: 302
Found by: Megacruncher
db: batch=77, k=14, 118 34 10 76 10 40

STPT(10)	1270573367339748677	0 2 72 74 102 104 132 134 204 206	-1950832017624
SPT(16)	1270573507092998429	0 62 68 114 122 150 168 198 224 254 272 300 308 354 360 422	-1811078767872
STPT(10)	1270573828497541619	0 2 18 20 30 32 42 44 60 62	-1489674224682
SPT(16)	1270573876331889851	0 8 42 50 56 60 66 80 198 212 218 222 228 236 270 278	-1441839876450
TPT(14)	1270574475478038371	0 2 18 20 60 62 90 92 156 158 168 170 258 260	-842693727930
TPT(14)	1270575173124009089	0 2 30 32 78 80 108 110 150 152 318 320 372 374	-145047757212
SPT(16)	1270575341552755039	0 22 42 58 90 102 148 162 208 222 268 280 312 328 348 370	23380988738
STPT(10)	1270575629108775791	0 2 6 8 48 50 90 92 96 98	310937009490
TPT(14)	1270575641384757269	0 2 48 50 78 80 90 92 168 170 240 242 282 284	323212990968
SPT(18)	1270575674284012697	0 12 14 116 122 132 144 164 206 210 252 272 284 294 300 402 404 416	356112246396
SPT(18)	1270575775372495619	0 2 14 54 98 104 150 152 174 188 210 212 258 264 308 348 360 362	457200729318