Dozenal Wiki
Register
Edit Page
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.

Latest revision Your text
Line 305: Line 305:
 
The density of primes end with 1 is relatively low (< 1/4), but the density of primes end with 5, 7 and E are nearly equal (all are a little more than 1/4). (i.e. for a given natural number ''N'', the number of primes end with 1 less than ''N'' is usually smaller than the number of primes end with 5 (or 7, or E) less than ''N'') e.g. For all 1426 primes < 10000, there are 3E8 primes (2E.3%) end with 1, 410 primes (30.3%) end with 5, 412 primes (30.5%) end with 7, 406 primes (2E.E%) end with E. It is conjectured that for every natural number ''N'' β‰₯ 10, the number of primes end with 1 less than ''N'' is smaller than the number of primes end with 5 (or 7, or E) less than ''N''. (Note: the [[percentage]] in this section are also in dozenal, i.e. 20% means 0.2 or 20/100 = 1/6, 36% means 0.36 or 36/100 = 7/20, 58.7% means 0.587 or 587/1000)
 
The density of primes end with 1 is relatively low (< 1/4), but the density of primes end with 5, 7 and E are nearly equal (all are a little more than 1/4). (i.e. for a given natural number ''N'', the number of primes end with 1 less than ''N'' is usually smaller than the number of primes end with 5 (or 7, or E) less than ''N'') e.g. For all 1426 primes < 10000, there are 3E8 primes (2E.3%) end with 1, 410 primes (30.3%) end with 5, 412 primes (30.5%) end with 7, 406 primes (2E.E%) end with E. It is conjectured that for every natural number ''N'' β‰₯ 10, the number of primes end with 1 less than ''N'' is smaller than the number of primes end with 5 (or 7, or E) less than ''N''. (Note: the [[percentage]] in this section are also in dozenal, i.e. 20% means 0.2 or 20/100 = 1/6, 36% means 0.36 or 36/100 = 7/20, 58.7% means 0.587 or 587/1000)
   
βˆ’
13665 is the smallest prime ''p'' such that the number of primes end with 1 or 5 ≀ ''p'' is more than the number of primes end with 3, 7 or E ≀ ''p'' (i.e. congruent to 1 or 3 mod 4, see <ref>[https://oeis.org/A007350]</ref>, of course, 3 is the only prime ends with 3). Besides, 9X03693X831 is the smallest prime ''p'' such that the number of primes end with 1 or 7 ≀ ''p'' is more than the number of primes end with 2, 5 or E ≀ ''p'' (i.e. congruent to 1 or 2 mod 3, see <ref>[https://oeis.org/A007352]</ref>, of course, 2 is the only prime ends with 2). Besides, 2E69E is the smallest prime ''p'' such that the number of primes end with 1 or E ≀ ''p'' is more than the number of primes end with 5 or 7 ≀ ''p'' (of course, 2 is the only prime ends with 2, and 3 is the only prime ends with 3). '''Question: What is the smallest prime ''p'' such that the number of primes end with 1 ≀ ''p'' is more than the number of primes end with ''d'' ≀ ''p'' for at least one of ''d'' = 5, 7 or E?'''
+
13665 is the smallest prime ''p'' such that the number of primes end with 1 or 5 ≀ ''p'' is more than the number of primes end with 3, 7 or E ≀ ''p'' (see <ref>[https://oeis.org/A007350]</ref>, of course, 3 is the only prime ends with 3). Besides, 9X03693X831 is the smallest prime ''p'' such that the number of primes end with 1 or 7 ≀ ''p'' is more than the number of primes end with 2, 5 or E ≀ ''p'' (see <ref>[https://oeis.org/A007352]</ref>, of course, 2 is the only prime ends with 2). Besides, 2E69E is the smallest prime ''p'' such that the number of primes end with 1 or E ≀ ''p'' is more than the number of primes end with 5 or 7 ≀ ''p'' (of course, 2 is the only prime ends with 2, and 3 is the only prime ends with 3). '''Question: What is the smallest prime ''p'' such that the number of primes end with 1 ≀ ''p'' is more than the number of primes end with ''d'' ≀ ''p'' for at least one of ''d'' = 5, 7 or E?'''
   
 
{|class="wikitable"
 
{|class="wikitable"
Please note that all contributions to the Dozenal Wiki are considered to be released under the CC-BY-SA
Cancel Editing help (opens in new window)