Prime p₀= 2150524203010149011 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 40 2 28 2 118 2 28 2 58 2 (?)
a_n: 0 2 66 68 108 110 138 140 258 260 288 290 348 350
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: 350
Found by: Xenon
db: batch=81, k=14, 64 40 28 118 28 58

TPT(14)	2150522684014142861	0 2 78 80 96 98 168 170 216 218 288 290 300 302	-1518996006150
SPT(16)	2150523254777559911	0 2 12 18 36 56 72 78 110 116 132 152 170 176 186 188	-948232589100
SPT(16)	2150523438477019141	0 18 46 70 76 90 138 142 156 160 208 222 228 252 280 298	-764533129870
STPT(10)	2150523657745219751	0 2 36 38 78 80 120 122 156 158	-545264929260
STPT(10)	2150523725011310651	0 2 30 32 60 62 90 92 120 122	-477998838360
STPT(10)	2150523745978465769	0 2 18 20 30 32 42 44 60 62	-457031683242
SPT(16)	2150524290970009319	0 18 32 50 68 78 80 122 138 180 182 192 210 228 242 260	87959860308
SPT(16)	2150524869141092273	0 20 86 90 98 104 126 128 216 218 240 246 254 258 324 344	666130943262
SPT(16)	2150525229290533429	0 28 52 54 70 78 88 102 130 144 154 162 178 180 204 232	1026280384418
SPT(16)	2150525386185769589	0 2 44 62 72 84 98 150 152 204 218 230 240 258 300 302	1183175620578
SPT(16)	2150525842215091337	0 12 24 36 50 54 120 162 254 296 362 366 380 392 404 416	1639204942326