Prime p₀= 1458656548757317277 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 46 2 28 2 88 2 40 2 (?)
a_n: 0 2 30 32 54 56 102 104 132 134 222 224 264 266
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: 266
Found by: [SG-2W]Kurzer
db: batch=78, k=14, 28 22 46 28 88 40

STPT(10)	1458656014738832807	0 2 42 44 72 74 102 104 144 146	-534018484470
STPT(10)	1458656091354613979	0 2 42 44 60 62 78 80 120 122	-457402703298
STPT(10)	1458656148689651279	0 2 18 20 30 32 42 44 60 62	-400067665998
TPT(14)	1458656283661740047	0 2 42 44 54 56 84 86 150 152 342 344 372 374	-265095577230
STPT(10)	1458656287216641167	0 2 30 32 72 74 114 116 144 146	-261540676110
SPT(13)	1458656346910912631	0 18 48 60 102 108 150 192 198 240 252 282 300	-201846404646
SPT(16)	1458656903279416879	0 10 12 22 24 78 112 114 148 150 184 238 240 250 252 262	354522099602
SPT(16)	1458656920295442193	0 6 16 28 54 100 118 120 124 126 144 190 216 228 238 244	371538124916
TPT(14)	1458656955289583207	0 2 90 92 114 116 132 134 240 242 270 272 354 356	406532265930
STPT(10)	1458657019408997657	0 2 12 14 42 44 72 74 84 86	470651680380
SPT(16)	1458657155280710213	0 54 78 86 96 98 110 170 174 234 246 248 258 266 290 344	606523392936