<div dir="ltr">Finally - integer radix (minimum 4-bits of headroom for 32-bit and 64-bit) primes, grouped into byte sizes, non-dominated set. 28/27 candidates (one of the 114 bit candidates is dominated, not sure which). Are there recommended limits on the small 'c' in Crandall primes? This list is only up to 32, but many on the SafeCurves list are in the 100s.<div><br></div><div><div><font face="courier new, monospace">Prime mod bytes 32-bit 64-bit</font></div><div><font face="courier new, monospace"> 2^850 - 3 5 128 34x25 17x50</font></div><div><font face="courier new, monospace"> 2^848 - 17 3 128 53x16 16x53</font></div><div><font face="courier new, monospace"> 2^810 - 5 3 128 30x27 15x54</font></div><div><font face="courier new, monospace"> 2^729 - 9 3 96 27x27 27x27</font></div><div><font face="courier new, monospace"> 2^689 - 3 5 96 53x13 13x53</font></div><div><font face="courier new, monospace"> 2^550 - 5 3 96 22x25 10x55</font></div><div><font face="courier new, monospace"> 2^546 - 11 5 96 21x26 13x42</font></div><div><font face="courier new, monospace"> 2^480 - 2^240 - 1 3 64 20x24 8x60</font></div><div><font face="courier new, monospace"> 2^468 - 17 3 64 18x26 9x52</font></div><div><font face="courier new, monospace">*2^448 - 2^224 - 1 3 64 16x28 8x56</font></div><div><font face="courier new, monospace"> 2^336 - 3 5 48 12x28 6x56</font></div><div><font face="courier new, monospace"> 2^285 - 9 3 48 15x19 5x57</font></div><div><font face="courier new, monospace">*2^255 - 19 5 32 15x17 5x51</font></div><div><font face="courier new, monospace"> 2^243 - 9 3 32 9x27 9x27</font></div><div><font face="courier new, monospace"> 2^230 - 27 5 32 10x23 5x46</font></div><div><font face="courier new, monospace"> 2^216 - 2^108 - 1 3 32 8x27 4x54</font></div><div><font face="courier new, monospace"> 2^190 - 11 5 24 10x19 5x38</font></div><div><font face="courier new, monospace"> 2^189 - 25 3 24 7x27 7x27</font></div><div><font face="courier new, monospace"> 2^171 - 19 5 24 9x19 3x57</font></div><div><font face="courier new, monospace"> 2^152 - 17 3 24 8x19 4x38</font></div><div><font face="courier new, monospace"> 2^150 - 3 5 24 6x25 3x50</font></div><div><font face="courier new, monospace"> 2^140 - 27 5 24 5x28 4x35</font></div><div><font face="courier new, monospace"> 2^125 - 9 3 16 5x25 5x25</font></div><div><font face="courier new, monospace"> 2^114 - 2^57 - 1 3 16 6x19 2x57</font></div><div><font face="courier new, monospace"> 2^114 - 11 5 16 6x19 2x57</font></div><div><font face="courier new, monospace"> 2^110 - 21 3 16 5x22 2x55</font></div><div><font face="courier new, monospace"> 2^104 - 17 3 16 4x26 2x52</font></div><div><font face="courier new, monospace"> 2^96 - 17 3 12 4x24 2x48</font></div></div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On 29 October 2014 10:37, Ben Harris <span dir="ltr"><<a href="mailto:mail@bharr.is" target="_blank">mail@bharr.is</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div><font face="courier new, monospace">Including Ridinghoods, and preferring 3 mod 4 over 1 mod 4 when all else is equal nets 57.</font></div><span class=""><div><br></div><div><font face="courier new, monospace">prime mod 4 28 32 58</font><br></div></span><div><div><span class=""><div><font face="courier new, monospace">2^96 - 17 3 4 3 2</font></div></span><span class=""><div><font face="courier new, monospace">2^110 - 21 3 4 4 2</font></div></span><div><font face="courier new, monospace">2^114 - 2^57 - 1 3 5 4 2</font></div><span class=""><div><font face="courier new, monospace">2^116 - 3 1 5 4 2</font></div></span><span class=""><div><font face="courier new, monospace">2^127 - 1 3 5 4 3</font></div><div><font face="courier new, monospace">2^137 - 13 3 5 5 3</font></div><div><font face="courier new, monospace">2^140 - 27 1 5 5 3</font></div><div><font face="courier new, monospace">2^152 - 17 3 6 5 3</font></div><div><font face="courier new, monospace">2^158 - 15 1 6 5 3</font></div><div><font face="courier new, monospace">2^166 - 5 3 6 6 3</font></div><div><font face="courier new, monospace">2^174 - 3 1 7 6 3</font></div><div><font face="courier new, monospace">2^189 - 25 3 7 6 4</font></div><div><font face="courier new, monospace">2^191 - 19 1 7 6 4</font></div><div><font face="courier new, monospace">2^196 - 15 1 7 7 4</font></div></span><div><font face="courier new, monospace">2^216 - 2^108 - 1 3 8 7 4</font></div><span class=""><div><font face="courier new, monospace">2^221 - 3 1 8 7 4</font></div><div><font face="courier new, monospace">2^226 - 5 3 9 8 4</font></div><div><font face="courier new, monospace">2^230 - 27 1 9 8 4</font></div></span><span class=""><div><font face="courier new, monospace">2^251 - 9 3 9 8 5</font></div><div><font face="courier new, monospace">2^255 - 19 1 10 8 5</font></div><div><font face="courier new, monospace">2^266 - 3 1 10 9 5</font></div><div><font face="courier new, monospace">2^285 - 9 3 11 9 5</font></div><div><font face="courier new, monospace">2^291 - 19 1 11 10 6</font></div></span><div><font face="courier new, monospace">2^322 - 2^161 - 1 3 12 11 6</font></div><span class=""><div><font face="courier new, monospace">2^336 - 3 1 12 11 6</font></div><div><font face="courier new, monospace">2^338 - 15 1 13 11 6</font></div><div><font face="courier new, monospace">2^369 - 25 3 14 12 7</font></div><div><font face="courier new, monospace">2^383 - 31 1 14 12 7</font></div><div><font face="courier new, monospace">2^389 - 21 3 14 13 7</font></div><div><font face="courier new, monospace">2^401 - 31 1 15 13 7</font></div></span><div><font face="courier new, monospace">2^416 - 2^208 - 1 3 15 13 8</font></div><div><font face="courier new, monospace">2^448 - 2^224 - 1 3 16 14 8</font></div><div><font face="courier new, monospace">2^450 - 2^225 - 1 3 17 15 8</font></div><span class=""><div><font face="courier new, monospace">2^452 - 3 1 17 15 8</font></div><div><font face="courier new, monospace">2^468 - 17 3 17 15 9</font></div></span><div><font face="courier new, monospace">2^480 - 2^240 - 1 3 18 15 9</font></div><span class=""><div><font face="courier new, monospace">2^489 - 21 3 18 16 9</font></div><div><font face="courier new, monospace">2^495 - 31 1 18 16 9</font></div><div><font face="courier new, monospace">2^521 - 1 3 19 17 9</font></div><div><font face="courier new, monospace">2^529 - 31 1 19 17 10</font></div><div><font face="courier new, monospace">2^537 - 9 3 20 17 10</font></div></span><span class=""><div><font face="courier new, monospace">2^550 - 5 3 20 18 10</font></div><div><font face="courier new, monospace">2^563 - 9 3 21 18 10</font></div><div><font face="courier new, monospace">2^583 - 27 1 21 19 11</font></div><div><font face="courier new, monospace">2^607 - 1 3 22 19 11</font></div><div><font face="courier new, monospace">2^610 - 27 1 22 20 11</font></div><div><font face="courier new, monospace">2^620 - 15 1 23 20 11</font></div><div><font face="courier new, monospace">2^664 - 17 3 24 21 12</font></div><div><font face="courier new, monospace">2^694 - 3 1 25 22 12</font></div><div><font face="courier new, monospace">2^699 - 9 3 25 22 13</font></div></span><span class=""><div><font face="courier new, monospace">2^717 - 25 3 26 23 13</font></div><div><font face="courier new, monospace">2^729 - 9 3 27 23 13</font></div><div><font face="courier new, monospace">2^810 - 5 3 29 26 14</font></div><div><font face="courier new, monospace">2^848 - 17 3 31 27 15</font></div><div><font face="courier new, monospace">2^850 - 3 1 31 27 15</font></div><div><font face="courier new, monospace">2^869 - 21 3 32 28 15</font></div><div><font face="courier new, monospace">2^923 - 31 1 33 29 16</font></div></span></div></div></div></div>
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