Prime p₀= 2864796233161002821 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 10 2 4 2 52 2 64 2 10 2 (?)
a_n: 0 2 18 20 30 32 36 38 90 92 156 158 168 170
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: 170
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 16 10 4 52 64 10

SPT(16)	2864794853565545191	0 90 96 100 106 126 148 156 172 180 202 222 228 232 238 328	-1379595457630
SPT(16)	2864795123668059707	0 24 26 116 140 164 210 236 240 266 312 336 360 450 452 476	-1109492943114
SPT(16)	2864795764545094351	0 12 46 66 108 112 126 130 138 142 156 160 202 222 256 268	-468615908470
SPT(16)	2864796120872073511	0 16 28 40 76 96 100 118 168 186 190 210 246 258 270 286	-112288929310
STPT(10)	2864796175909716857	0 2 12 14 72 74 132 134 144 146	-57251285964
TPT(14)	2864796231674860541	0 2 48 50 120 122 126 128 156 158 168 170 216 218	-1486142280
STPT(10)	2864796633890787521	0 2 30 32 78 80 126 128 156 158	400729784700
STPT(10)	2864797182520521011	0 2 30 32 78 80 126 128 156 158	949359518190
STPT(10)	2864797220166315911	0 2 36 38 78 80 120 122 156 158	987005313090
STPT(10)	2864797497839580629	0 2 18 20 30 32 42 44 60 62	1264678577808
STPT(10)	2864798363602432709	0 2 12 14 90 92 168 170 180 182	2130441429888