Prime p₀= 1144368298912276049 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 16 2 202 2 88 2 64 2 (?)
a_n: 0 2 78 80 120 122 138 140 342 344 432 434 498 500
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: 500
Found by: Polaxis
db: batch=76, k=14, 76 40 16 202 88 64

SPT(16)	1144366516093624961	0 36 48 86 90 96 102 120 278 296 302 308 312 350 362 398	-1782818651088
SPT(16)	1144366712077547143	0 16 34 40 70 84 100 106 174 180 196 210 240 246 264 280	-1586834728906
SPT(16)	1144367107515090703	0 24 30 54 58 70 100 114 124 138 168 180 184 208 214 238	-1191397185346
SPT(16)	1144367416411904257	0 4 42 46 82 84 94 96 100 102 112 114 150 154 192 196	-882500371792
STPT(10)	1144367621643155969	0 2 42 44 90 92 138 140 180 182	-677269120080
SPT(16)	1144368056916673181	0 36 50 60 98 120 126 132 236 242 248 270 308 318 332 368	-241995602868
STPT(10)	1144368655442285549	0 2 48 50 90 92 132 134 180 182	356530009500
SPT(16)	1144368662815644421	0 12 36 42 70 82 96 126 136 166 180 192 220 226 250 262	363903368372
STPT(12)	1144368775668080057	0 2 12 14 42 44 102 104 132 134 144 146	476755804008
STPT(10)	1144368803442100961	0 2 6 8 48 50 90 92 96 98	504529824912
STPT(10)	1144368812172327587	0 2 24 26 42 44 60 62 84 86	513260051538