Prime p₀= 727260184413049751 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 52 2 28 2 136 2 100 2 4 2 (?)
a_n: 0 2 6 8 60 62 90 92 228 230 330 332 336 338
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: 338
Found by: Theadalus
db: batch=73, k=14, 4 52 28 136 100 4

SPT(16)	727258522342871513	0 44 54 78 98 128 158 176 228 246 276 306 326 350 360 404	-1662070178238
STPT(10)	727258526907347957	0 2 30 32 42 44 54 56 84 86	-1657505701794
SPT(16)	727258796921726023	0 54 66 70 78 96 114 136 168 190 208 226 234 238 250 304	-1387491323728
SPT(16)	727258979229221573	0 24 44 50 54 78 128 138 140 150 200 224 228 234 254 278	-1205183828178
STPT(10)	727259746431984131	0 2 36 38 78 80 120 122 156 158	-437981065620
SPT(16)	727260114601186259	0 60 62 80 98 104 108 224 378 494 498 504 522 540 542 602	-69811863492
SPT(16)	727260273241809941	0 6 12 30 36 72 110 132 140 162 200 236 242 260 266 272	88828760190
SPT(16)	727260383780271493	0 6 18 34 40 48 78 84 130 136 166 174 180 196 208 214	199367221742
STPT(10)	727260529265915969	0 2 18 20 30 32 42 44 60 62	344852866218
TPT(14)	727260541809077321	0 2 36 38 48 50 66 68 78 80 126 128 138 140	357396027570
STPT(10)	727260995036602067	0 2 30 32 42 44 54 56 84 86	810623552316