Prime p₀= 2253443980465838009 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 10 2 58 2 58 2 40 2 34 2 (?)
a_n: 0 2 78 80 90 92 150 152 210 212 252 254 288 290
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: 290
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 76 10 58 58 40 34

SPT(18)	2253442065398940257	0 20 24 56 132 150 176 200 206 210 216 240 266 284 360 392 396 416	-1915066897752
STPT(10)	2253442184858174411	0 2 6 8 48 50 90 92 96 98	-1795607663598
SPT(16)	2253443354429654063	0 14 26 98 146 176 204 260 264 320 348 378 426 498 510 524	-626036183946
SPT(16)	2253443355770089547	0 12 32 72 74 84 86 116 120 150 152 162 164 204 224 236	-624695748462
STPT(10)	2253443469954807341	0 2 30 32 78 80 126 128 156 158	-510511030668
SPT(16)	2253443476646008369	0 34 94 118 162 198 202 238 324 360 364 400 444 468 528 562	-503819829640
TPT(14)	2253444030220399691	0 2 6 8 78 80 138 140 306 308 330 332 510 512	49754561682
TPT(14)	2253444392886264761	0 2 66 68 78 80 96 98 126 128 138 140 150 152	412420426752
STPT(10)	2253444758978211749	0 2 18 20 30 32 42 44 60 62	778512373740
STPT(10)	2253444883300534667	0 2 72 74 102 104 132 134 204 206	902834696658
STPT(10)	2253445404864653771	0 2 36 38 78 80 120 122 156 158	1424398815762