Prime p₀= 936598730656958111 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 46 2 58 2 106 2 70 2 58 2 (?)
a_n: 0 2 30 32 78 80 138 140 246 248 318 320 378 380
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: 380
Found by: Theadalus
db: batch=76, k=14, 28 46 58 106 70 58

SPT(16)	936597727851039643	0 4 60 90 138 198 204 208 246 250 256 316 364 394 450 454	-1002805918468
STPT(10)	936597852221518517	0 2 30 32 60 62 90 92 120 122	-878435439594
STPT(10)	936597864083128277	0 2 30 32 60 62 90 92 120 122	-866573829834
SPT(16)	936598149920698423	0 30 58 60 90 130 144 160 264 280 294 334 364 366 394 424	-580736259688
STPT(10)	936598361817784121	0 2 30 32 78 80 126 128 156 158	-368839173990
SPT(16)	936598461027056879	0 8 20 44 62 78 84 90 122 128 134 150 168 192 204 212	-269629901232
SPT(16)	936599620411264297	0 94 120 132 180 192 202 222 232 252 262 274 322 334 360 454	889754306186
STPT(10)	936599773718767421	0 2 30 32 168 170 306 308 336 338	1043061809310
SPT(20)	936599841675193361	0 12 18 66 108 116 152 156 198 242 246 290 332 336 372 380 422 470 476 488	1111018235250
STPT(10)	936600272938633967	0 2 42 44 72 74 102 104 144 146	1542281675856
SPT(16)	936600298711523179	0 42 54 88 90 94 114 160 192 238 258 262 264 298 310 352	1568054565068