20200601, 22:37  #12 
May 2018
3^{3}×7 Posts 
Yes. 282332382833 is a cool number. It reminds me of the maximal prime gap between 352521223451364323 and 352521223451365651, and the maximal prime gap after 6787988999657777797.

20200603, 16:38  #13  
Nov 2016
2^{2}·541 Posts 
Quote:
For primitive root 2, a gap of 8k+4 does not exist, since all primes having primitive root 2 are == 3, 5 (mod 8) Code:
gap prime 2 3 6 5 8 29 10 19 14 149 16 37 18 83 22 421 24 107 26 587 30 317 32 2099 34 619 38 2621 40 1693 42 227 46 1381 48 709 50 3203 54 2477 56 4547 58 12979 62 4157 64 4723 66 1307 70 4021 72 947 74 1787 78 5573 80 12659 82 23251 86 20357 88 9949 90 13523 94 18493 96 15971 98 14243 102 33637 104 3083 106 63667 110 20789 112 24547 114 9059 118 88093 120 11317 122 109619 126 70717 128 46349 130 49891 134 244109 136 70237 138 105691 142 132709 144 18269 146 425387 150 221261 152 266117 154 62323 158 235541 160 31699 162 139907 166 102877 168 65371 170 142211 174 199037 176 265163 178 296299 182 223829 184 411013 186 137723 190 699757 192 191837 194 658643 198 103093 200 339827 202 302227 206 2989757 208 806581 210 425603 214 155797 216 598427 218 184259 222 736469 224 514949 226 2373307 230 1530293 232 1078411 234 512819 238 1427509 240 370133 242 1353371 246 2084653 248 476603 250 2551099 254 4013573 256 2617651 

20200603, 18:00  #14  
Dec 2008
you know...around...
13·43 Posts 
Quote:
You could calculate the merits via Artin*gap/log(p) and look for bounds in the CSG analogue Artin*gap/logĀ²(p). It'd be interesting to see if there are some extraordinarily large gaps. If not in base 2, you could check other bases as well. 

20200630, 12:42  #15  
Nov 2016
2^{2}·541 Posts 
Quote:


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