Prime p₀= 2259059396185251017 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 28 2 16 2 40 2 94 2 (?)
a_n: 0 2 12 14 24 26 54 56 72 74 114 116 210 212
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: 212
Found by: Landjunge
db: batch=81, k=14, 10 10 28 16 40 94

SPT(16)	2259058913841645529	0 28 34 132 138 174 210 220 252 262 298 334 340 438 444 472	-482343605488
STPT(10)	2259059007017739107	0 2 30 32 42 44 54 56 84 86	-389167511910
SPT(16)	2259059076099489383	0 24 54 56 66 96 114 126 128 140 158 188 198 200 230 254	-320085761634
SPT(16)	2259059145734432779	0 34 52 100 108 114 118 124 168 174 178 184 192 240 258 292	-250450818238
SPT(16)	2259059178376780303	0 28 60 66 88 96 144 150 154 160 208 216 238 244 276 304	-217808470714
SPT(16)	2259059221310623211	0 2 20 30 98 140 176 186 242 252 288 330 398 408 426 428	-174874627806
STPT(10)	2259060029486740691	0 2 30 32 78 80 126 128 156 158	633301489674
STPT(10)	2259060510503588717	0 2 120 122 162 164 204 206 324 326	1114318337700
SPT(16)	2259060760217470463	0 66 104 114 128 140 158 170 204 216 234 246 260 270 308 374	1364032219446
SPT(16)	2259060806348942059	0 72 84 112 120 150 172 210 214 252 274 304 312 340 352 424	1410163691042
SPT(16)	2259060850498097267	0 12 42 62 66 116 194 200 216 222 300 350 354 374 404 416	1454312846250