Prime p₀= 729069202995295289 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 58 2 88 2 76 2 10 2 64 2 (?)
a_n: 0 2 12 14 72 74 162 164 240 242 252 254 318 320
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: 320
Found by: MarkRBright
db: batch=73, k=14, 10 58 88 76 10 64

SPT(16)	729068099656438063	0 18 40 54 78 114 156 184 210 238 280 316 340 354 376 394	-1103338857226
SPT(16)	729068644117066753	0 36 40 58 64 78 90 126 148 184 196 210 216 234 238 274	-558878228536
STPT(10)	729068882282328491	0 2 36 38 78 80 120 122 156 158	-320712966798
STPT(10)	729068970940483037	0 2 42 44 72 74 102 104 144 146	-232054812252
SPT(16)	729069073085295473	0 18 24 128 164 194 216 264 410 458 480 510 546 650 656 674	-129909999816
STPT(10)	729069192353736989	0 2 18 20 30 32 42 44 60 62	-10641558300
STPT(10)	729069469169008577	0 2 30 32 42 44 54 56 84 86	266173713288
SPT(20)	729069739917760529	0 8 12 60 92 122 138 182 210 222 248 260 288 332 348 378 410 458 462 470	536922465240
STPT(10)	729070392182406689	0 2 18 20 30 32 42 44 60 62	1189187111400
SPT(18)	729070416925528967	0 2 42 86 126 132 144 182 186 200 204 242 254 260 300 344 384 386	1213930233678
STPT(10)	729070695457971071	0 2 6 8 18 20 30 32 36 38	1492462675782