Prime p₀= 2565933969617613629 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 40 2 46 2 16 2 10 2 58 2 (?)
a_n: 0 2 60 62 102 104 150 152 168 170 180 182 240 242
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: 242
Found by: Arkhenia
db: batch=82, k=14, 58 40 46 16 10 58

SPT(18)	2565933077506016957	0 26 62 84 102 120 146 204 216 230 242 300 326 344 362 384 420 446	-892111596672
STPT(10)	2565933090763539797	0 2 24 26 42 44 60 62 84 86	-878854073832
SPT(16)	2565933640100262577	0 6 36 40 52 84 96 112 144 160 172 204 216 220 250 256	-329517351052
SPT(16)	2565933642711060229	0 12 48 72 112 138 144 174 178 208 214 240 280 304 340 352	-326906553400
STPT(12)	2565933673082645609	0 2 30 32 42 44 198 200 210 212 240 242	-296534968020
SPT(16)	2565933680438528087	0 30 32 56 72 120 140 162 254 276 296 344 360 384 386 416	-289179085542
SPT(16)	2565934255855898861	0 20 30 38 62 68 90 98 162 170 192 198 222 230 240 260	286238285232
STPT(10)	2565934279256096891	0 2 6 8 18 20 30 32 36 38	309638483262
STPT(10)	2565934554730344527	0 2 30 32 72 74 114 116 144 146	585112730898
SPT(16)	2565934683063537473	0 30 78 150 156 164 186 206 288 308 330 338 344 416 464 494	713445923844
SPT(16)	2565934772214828517	0 6 54 60 72 76 94 96 130 132 150 154 166 172 220 226	802597214888