Prime p₀= 1563827868738327107 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 52 2 94 2 22 2 28 2 46 2 (?)
a_n: 0 2 60 62 114 116 210 212 234 236 264 266 312 314
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: 314
Found by: xii5ku
db: batch=78, k=14, 58 52 94 22 28 46

TPT(14)	1563825748401178739	0 2 72 74 78 80 120 122 162 164 222 224 240 242	-2120337148368
SPT(16)	1563826725368612077	0 36 72 120 142 172 196 202 240 246 270 300 322 370 406 442	-1143369715030
SPT(16)	1563827215377338063	0 8 26 50 78 96 110 116 210 216 230 248 276 300 318 326	-653360989044
SPT(16)	1563827220541360231	0 6 22 30 48 70 78 132 136 190 198 220 238 246 262 268	-648196966876
STPT(10)	1563827224952890967	0 2 24 26 42 44 60 62 84 86	-643785436140
STPT(10)	1563827277425999141	0 2 6 8 48 50 90 92 96 98	-591312327966
STPT(10)	1563828129609130601	0 2 150 152 168 170 186 188 336 338	260870803494
STPT(10)	1563828264812053127	0 2 24 26 42 44 60 62 84 86	396073726020
SPT(16)	1563828595695275887	0 22 52 70 76 82 90 96 106 112 120 126 132 150 180 202	726956948780
SPT(16)	1563828842721087119	0 38 62 78 90 108 134 150 182 198 224 242 254 270 294 332	973982760012
SPT(16)	1563829187993927627	0 14 24 42 86 90 146 164 222 240 296 300 344 362 372 386	1319255600520