Prime p₀= 2819097957079079237 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 28 2 28 2 28 2 70 2 34 2 (?)
a_n: 0 2 42 44 72 74 102 104 132 134 204 206 240 242
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: [SG-FC] hl
db: batch=82, k=14, 40 28 28 28 70 34

SPT(16)	2819096330646166303	0 36 46 118 120 148 168 196 210 238 258 286 288 360 370 406	-1626432912934
SPT(16)	2819096394126885269	0 38 50 60 62 78 90 108 242 260 272 288 290 300 312 350	-1562952193968
SPT(16)	2819096599844467927	0 22 24 46 52 96 102 124 132 154 160 204 210 232 234 256	-1357234611310
STPT(10)	2819096693864103941	0 2 36 38 78 80 120 122 156 158	-1263214975296
STPT(10)	2819097458525971307	0 2 24 26 42 44 60 62 84 86	-498553107930
STPT(10)	2819097793923612527	0 2 42 44 72 74 102 104 144 146	-163155466710
STPT(10)	2819098306520378327	0 2 30 32 42 44 54 56 84 86	349441299090
TPT(14)	2819098403529842009	0 2 42 44 78 80 90 92 102 104 120 122 132 134	446450762772
SPT(16)	2819098579889438261	0 20 50 56 108 116 126 150 158 182 192 200 252 258 288 308	622810359024
SPT(16)	2819098740911927867	0 66 84 96 162 186 242 294 362 414 470 494 560 572 590 656	783832848630
TPT(14)	2819098763767815161	0 2 6 8 78 80 150 152 180 182 216 218 276 278	806688735924