Prime p₀= 782499414103680461 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 16 2 10 2 28 2 28 2 136 2 (?)
a_n: 0 2 108 110 126 128 138 140 168 170 198 200 336 338
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: 338
Found by: [SG]FX
db: batch=73, k=14, 106 16 10 28 28 136

SPT(16)	782498856816954437	0 2 12 44 84 110 132 146 150 164 186 212 252 284 294 296	-557286726024
SPT(16)	782499101471864071	0 52 60 72 88 148 168 190 270 292 312 372 388 400 408 460	-312631816390
STPT(12)	782499171081062117	0 2 12 14 42 44 60 62 90 92 102 104	-243022618344
SPT(16)	782499251525996033	0 24 78 128 138 144 164 194 210 240 260 266 276 326 380 404	-162577684428
SPT(13)	782499318282189653	0 54 60 78 84 120 144 168 204 210 228 234 288	-95821490808
STPT(10)	782499347033613689	0 2 18 20 30 32 42 44 60 62	-67070066772
STPT(10)	782499453134518487	0 2 30 32 42 44 54 56 84 86	39030838026
SPT(16)	782499481948828261	0 10 22 30 36 46 76 88 90 102 132 142 148 156 168 178	67845147800
TPT(14)	782499556205773979	0 2 18 20 72 74 102 104 108 110 138 140 180 182	142102093518
STPT(10)	782499613471755041	0 2 36 38 78 80 120 122 156 158	199368074580
SPT(16)	782499685132863821	0 12 36 48 78 90 92 120 158 186 188 200 230 242 266 278	271029183360