Prime p₀= 3029949854194318331 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 40 2 88 2 16 2 58 2 82 2 (?)
a_n: 0 2 126 128 168 170 258 260 276 278 336 338 420 422
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: 422
Found by: raddoc
db: batch=82, k=14, 124 40 88 16 58 82

SPT(18)	3029948386067659657	0 12 30 34 46 52 66 94 150 286 342 370 384 390 402 406 424 436	-1468126658674
SPT(16)	3029948850665201513	0 6 14 44 74 86 90 114 140 164 168 180 210 240 248 254	-1003529116818
SPT(16)	3029949247616787289	0 24 28 34 84 112 160 198 244 282 330 358 408 414 418 442	-606577531042
SPT(16)	3029949359838742171	0 18 28 76 136 150 172 178 210 216 238 252 312 360 370 388	-494355576160
STPT(10)	3029949570528972989	0 2 42 44 60 62 78 80 120 122	-283665345342
SPT(16)	3029949783310461197	0 32 90 104 116 120 132 170 186 224 236 240 252 266 324 356	-70883857134
TPT(16)	3029950001099047307	0 2 30 32 72 74 180 182 204 206 282 284 372 374 474 476	146904728976
TPT(14)	3029950146800606921	0 2 36 38 90 92 150 152 258 260 288 290 348 350	292606288590
SPT(16)	3029950192177216057	0 10 46 66 94 100 102 106 150 154 156 162 190 210 246 256	337982897726
STPT(10)	3029950211287152911	0 2 6 8 18 20 30 32 36 38	357092834580
SPT(13)	3029950294863050987	0 42 54 60 84 120 162 204 240 264 270 282 324	440668732656