Prime p₀= 2004364888209298649 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 76 2 52 2 76 2 10 2 28 2 (?)
a_n: 0 2 60 62 138 140 192 194 270 272 282 284 312 314
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: 314
Found by: Orange Kid
db: batch=80, k=14, 58 76 52 76 10 28

STPT(10)	2004362583921689699	0 2 78 80 120 122 162 164 240 242	-2304287608950
SPT(16)	2004362720067104363	0 30 158 170 186 200 218 246 290 318 336 350 366 378 506 536	-2168142194286
SPT(16)	2004362804180160481	0 10 12 18 58 150 208 210 280 282 340 432 472 478 480 490	-2084029138168
SPT(16)	2004363133101956833	0 16 34 76 118 120 126 156 238 268 274 276 318 360 378 394	-1755107341816
STPT(10)	2004363465749590997	0 2 72 74 102 104 132 134 204 206	-1422459707652
STPT(10)	2004363652946484041	0 2 36 38 78 80 120 122 156 158	-1235262814608
SPT(16)	2004365069743176863	0 60 74 98 108 114 128 140 144 156 170 176 186 210 224 284	181533878214
SPT(16)	2004365166347086729	0 28 82 102 142 154 174 180 202 208 228 240 280 300 354 382	278137788080
STPT(10)	2004365234280248129	0 2 42 44 90 92 138 140 180 182	346070949480
SPT(16)	2004365415393025849	0 42 72 108 118 138 162 178 222 238 262 282 292 328 358 400	527183727200
SPT(16)	2004365477797002037	0 6 54 82 100 130 196 204 292 300 366 396 414 442 490 496	589587703388