Prime p₀= 2015046140790415721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 10 2 94 2 58 2 82 2 76 2 (?)
a_n: 0 2 48 50 60 62 156 158 216 218 300 302 378 380
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: 380
Found by: Landjunge
db: batch=80, k=14, 46 10 94 58 82 76

SPT(16)	2015044828315744481	0 20 68 78 110 116 156 176 180 200 240 246 278 288 336 356	-1312474671240
STPT(10)	2015044910012361917	0 2 30 32 42 44 54 56 84 86	-1230778053804
SPT(16)	2015045030987617183	0 18 70 78 88 100 154 190 198 234 288 300 310 318 370 388	-1109802798538
STPT(10)	2015045822486488457	0 2 30 32 42 44 54 56 84 86	-318303927264
SPT(16)	2015045873762726473	0 34 70 78 84 100 154 190 378 414 468 484 490 498 534 568	-267027689248
SPT(16)	2015046050789028329	0 50 90 102 128 150 182 242 300 360 392 414 440 452 492 542	-90001387392
STPT(10)	2015047127525039747	0 2 60 62 72 74 84 86 144 146	986734624026
SPT(16)	2015047618839340097	0 12 36 84 90 96 104 110 126 132 140 146 152 200 224 236	1478048924376
SPT(16)	2015048984892329467	0 16 22 34 54 90 160 174 232 246 316 352 372 384 390 406	2844101913746
SPT(16)	2015049007589816479	0 24 30 42 64 72 138 142 150 154 220 228 250 262 268 292	2866799400758
STPT(10)	2015049072868782029	0 2 48 50 60 62 72 74 120 122	2932078366308