Prime p₀= 802802389406207009 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 76 2 10 2 118 2 34 2 88 2 (?)
a_n: 0 2 72 74 150 152 162 164 282 284 318 320 408 410
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: 410
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 70 76 10 118 34 88

SPT(16)	802801330743020237	0 14 30 56 66 102 104 156 200 252 254 290 300 326 342 356	-1058663186772
SPT(16)	802801481589421679	0 68 102 122 180 200 224 242 270 288 312 332 390 410 444 512	-907816785330
SPT(16)	802801815530520359	0 8 78 80 138 180 234 254 288 308 362 404 462 464 534 542	-573875686650
STPT(10)	802801834264048427	0 2 12 14 72 74 132 134 144 146	-555142158582
SPT(16)	802801868566821703	0 34 40 54 160 238 250 310 318 378 390 468 574 588 594 628	-520839385306
STPT(10)	802801937336674397	0 2 42 44 132 134 222 224 264 266	-452069532612
SPT(16)	802802696697252341	0 30 48 62 72 122 128 146 192 210 216 266 276 290 308 338	307291045332
SPT(16)	802802769114880669	0 10 48 64 78 90 142 148 204 210 262 274 288 304 342 352	379708673660
SPT(16)	802802831713202527	0 16 72 96 106 124 132 160 336 364 372 390 400 424 480 496	442306995518
SPT(16)	802802908550697053	0 18 68 114 116 128 198 206 438 446 516 528 530 576 626 644	519144490044
STPT(10)	802803099805401041	0 2 6 8 48 50 90 92 96 98	710399194032