Prime p₀= 2678643791453539829 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 28 2 28 2 52 2 16 2 40 2 (?)
a_n: 0 2 78 80 108 110 138 140 192 194 210 212 252 254
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: 254
Found by: [SG-FC] hl
db: batch=82, k=14, 76 28 28 52 16 40

STPT(10)	2678642172866288171	0 2 6 8 48 50 90 92 96 98	-1618587251658
TPT(14)	2678642293732276577	0 2 102 104 114 116 144 146 234 236 252 254 312 314	-1497721263252
STPT(10)	2678642302107051617	0 2 30 32 42 44 54 56 84 86	-1489346488212
STPT(10)	2678642767836606551	0 2 36 38 78 80 120 122 156 158	-1023616933278
SPT(16)	2678642971337222243	0 30 44 90 98 146 224 266 288 330 408 456 464 510 524 554	-820116317586
STPT(10)	2678643567160138481	0 2 36 38 78 80 120 122 156 158	-224293401348
STPT(10)	2678643868552489169	0 2 48 50 90 92 132 134 180 182	77098949340
STPT(10)	2678643931159100381	0 2 36 38 78 80 120 122 156 158	139705560552
SPT(16)	2678644494065953583	0 74 86 108 114 144 164 176 198 210 230 260 266 288 300 374	702612413754
STPT(10)	2678644597805447627	0 2 30 32 72 74 114 116 144 146	806351907798
SPT(16)	2678644673823868699	0 22 28 88 108 130 162 252 340 430 462 484 504 564 570 592	882370328870