Prime p₀= 1286011694850241787 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 28 2 10 2 28 2 64 2 (?)
a_n: 0 2 30 32 42 44 72 74 84 86 114 116 180 182
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: 182
Found by: Cruncher Pete
db: batch=77, k=14, 28 10 28 10 28 64

SPT(16)	1286010747072380233	0 6 58 66 120 154 190 196 198 204 240 274 328 336 388 394	-947777861554
TPT(16)	1286010765353125739	0 2 12 14 48 50 102 104 132 134 222 224 228 230 252 254	-929497116048
SPT(16)	1286010833600286217	0 12 22 30 64 102 106 142 144 180 184 222 256 264 274 286	-861249955570
STPT(10)	1286011180020969287	0 2 30 32 42 44 54 56 84 86	-514829272500
STPT(10)	1286011360915073621	0 2 6 8 48 50 90 92 96 98	-333935168166
STPT(10)	1286011661640187211	0 2 30 32 120 122 210 212 240 242	-33210054576
STPT(12)	1286011694850241787	0 2 30 32 42 44 72 74 84 86 114 116	0
STPT(10)	1286011806903893747	0 2 30 32 42 44 54 56 84 86	112053651960
SPT(16)	1286012738212041977	0 14 20 44 146 152 194 222 254 282 324 330 432 456 462 476	1043361800190
SPT(16)	1286013105926386613	0 6 90 96 174 200 216 240 254 278 294 320 398 404 488 494	1411076144826
STPT(10)	1286013165097356251	0 2 6 8 48 50 90 92 96 98	1470247114464