Prime p₀= 1144239254169336251 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 10 2 10 2 16 2 70 2 64 2 (?)
a_n: 0 2 66 68 78 80 90 92 108 110 180 182 246 248
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: 248
Found by: Putin Has a Small Dick
db: batch=76, k=14, 64 10 10 16 70 64

SPT(16)	1144237771272125141	0 6 8 30 36 42 68 80 138 150 176 182 188 210 212 218	-1482897211110
SPT(16)	1144237893301868341	0 12 28 58 72 78 82 96 172 186 190 196 210 240 256 268	-1360867467910
STPT(10)	1144237900223311391	0 2 36 38 78 80 120 122 156 158	-1353946024860
STPT(10)	1144238103705391991	0 2 6 8 18 20 30 32 36 38	-1150463944260
STPT(10)	1144238660317452611	0 2 6 8 18 20 30 32 36 38	-593851883640
STPT(12)	1144238887025836367	0 2 42 44 54 56 120 122 132 134 174 176	-367143499884
STPT(10)	1144239863517250469	0 2 12 14 30 32 48 50 60 62	609347914218
SPT(16)	1144239884850977071	0 22 70 108 132 136 160 198 280 318 342 346 370 408 456 478	630681640820
SPT(16)	1144240305470763031	0 18 72 100 102 112 130 168 202 240 258 268 270 298 352 370	1051301426780
SPT(16)	1144240546025315833	0 66 78 90 106 108 120 156 160 196 208 210 226 238 250 316	1291855979582
SPT(16)	1144240811285772307	0 6 60 70 100 132 142 162 184 204 214 246 276 286 340 346	1557116436056