Prime p₀= 2396302836789176039 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 28 2 4 2 28 2 70 2 16 2 (?)
a_n: 0 2 102 104 132 134 138 140 168 170 240 242 258 260
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: 260
Found by: JonS
db: batch=81, k=14, 100 28 4 28 70 16

SPT(16)	2396300842980733841	0 8 20 36 38 42 48 78 80 110 116 120 122 138 150 158	-1993808442198
SPT(16)	2396301733466380589	0 48 78 90 104 114 122 128 174 180 188 198 212 224 254 302	-1103322795450
SPT(16)	2396302040726655167	0 30 32 36 56 60 120 144 152 176 236 240 260 264 266 296	-796062520872
STPT(10)	2396302350735921539	0 2 18 20 30 32 42 44 60 62	-486053254500
SPT(16)	2396302424328246617	0 2 32 50 60 80 102 120 122 140 162 182 192 210 240 242	-412460929422
SPT(16)	2396302639488945653	0 36 50 74 114 126 246 354 410 518 638 650 690 714 728 764	-197300230386
STPT(10)	2396302951239515567	0 2 12 14 42 44 72 74 84 86	114450339528
SPT(16)	2396303694218077733	0 18 20 60 84 96 110 138 146 174 188 200 224 264 266 284	857428901694
TPT(14)	2396304116837309639	0 2 42 44 48 50 78 80 120 122 162 164 198 200	1280048133600
STPT(10)	2396304122685219947	0 2 30 32 72 74 114 116 144 146	1285896043908
SPT(20)	2396304930098334461	0 48 66 78 92 108 138 182 188 206 222 240 246 290 320 336 350 362 380 428	2093309158422