Prime p₀= 1270575641384757269 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 28 2 10 2 76 2 70 2 40 2 (?)
a_n: 0 2 48 50 78 80 90 92 168 170 240 242 282 284
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: Megacruncher
db: batch=77, k=14, 46 28 10 76 70 40

SPT(16)	1270573876331889851	0 8 42 50 56 60 66 80 198 212 218 222 228 236 270 278	-1765052867418
TPT(14)	1270574475478038371	0 2 18 20 60 62 90 92 156 158 168 170 258 260	-1165906718898
TPT(14)	1270575173124009089	0 2 30 32 78 80 108 110 150 152 318 320 372 374	-468260748180
TPT(14)	1270575318171766301	0 2 120 122 156 158 168 170 246 248 258 260 300 302	-323212990968
SPT(16)	1270575341552755039	0 22 42 58 90 102 148 162 208 222 268 280 312 328 348 370	-299832002230
STPT(10)	1270575629108775791	0 2 6 8 48 50 90 92 96 98	-12275981478
SPT(18)	1270575674284012697	0 12 14 116 122 132 144 164 206 210 252 272 284 294 300 402 404 416	32899255428
SPT(18)	1270575775372495619	0 2 14 54 98 104 150 152 174 188 210 212 258 264 308 348 360 362	133987738350
TPT(14)	1270575806202992039	0 2 60 62 78 80 102 104 240 242 288 290 342 344	164818234770
STPT(10)	1270575918591481937	0 2 30 32 42 44 54 56 84 86	277206724668
STPT(10)	1270576242337184747	0 2 30 32 42 44 54 56 84 86	600952427478