Prime p₀= 3015759301572836057 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 130 2 58 2 94 2 28 2 28 2 (?)
a_n: 0 2 72 74 204 206 264 266 360 362 390 392 420 422
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: 422
Found by: ginga
db: batch=82, k=14, 70 130 58 94 28 28

SPT(16)	3015757463289968393	0 6 14 20 86 96 140 156 188 204 248 258 324 330 338 344	-1838282867664
SPT(16)	3015757861989619709	0 42 48 54 74 138 188 198 254 264 314 378 398 404 410 452	-1439583216348
STPT(10)	3015757961652756557	0 2 12 14 42 44 72 74 84 86	-1339920079500
SPT(16)	3015758569746341183	0 14 18 24 30 36 50 66 98 114 128 134 140 146 150 164	-731826494874
SPT(16)	3015758602066158631	0 28 42 48 70 82 100 112 126 138 156 168 190 196 210 238	-699506677426
STPT(10)	3015758972184460217	0 2 60 62 102 104 144 146 204 206	-329388375840
SPT(16)	3015759365153824903	0 4 18 124 168 180 186 208 276 298 304 316 360 466 480 484	63580988846
SPT(16)	3015759432747287573	0 44 68 98 110 156 194 224 270 300 338 384 396 426 450 494	131174451516
STPT(10)	3015759498069310427	0 2 30 32 42 44 54 56 84 86	196496474370
SPT(16)	3015760587007129327	0 6 36 66 120 126 144 160 246 262 280 286 340 370 400 406	1285434293270
SPT(20)	3015760741401940669	0 22 48 82 112 144 174 184 190 202 210 222 228 238 268 300 330 364 390 412	1439829104612