Anonymous user
Talk:Brazilian numbers: Difference between revisions
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:: Thanks, Mr. Horst (userid Horst.h), I added (the non-prime hint) to the REXX program and it speeded it up by a factor of two. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 21:51, 15 August 2019 (UTC)
::: some more observations by factorization of the numbers:<BR>Brazilian primes always have "1" as digit.MaxBase = trunc(sqrt(prime))-> "111" and therefor are rare 213 out of 86400.<BR>So one need only to test if digit is "1" for prime numbers.
<pre>
number = factors base repeated digit
7 = 7 2 1 "111" to base 2
13 = 13 3 1 "111" to base 3
31 = 31 2 1 "11111" to base 2
43 = 43 6 1
73 = 73 8 1
127 = 127 2 1 "1111111" to base 2
157 = 157 12 1
--
601 = 601 24 1
757 = 757 27 1
1093 = 1093 3 1 "1111111" to base 3
...
987043 = 987043 993 1
1003003 = 1003003 1001 1
1005007 = 1005007 1002 1
1015057 = 1015057 1007 1
1023133 = 1023133 1011 1
1033273 = 1033273 1016 1
1041421 = 1041421 1020 1
1045507 = 1045507 1022 1
1059871 = 1059871 1029 1 "111" to base 1029
Max number 1084566 -> 84600 primes
Brazilian primes found 213</pre>
How about nonprime odd numbers?
<pre>
number = factors base repeated digit
15 = 3*5 2 1 = "1111" also "33" to base 4 -> ( 5-1)
21 = 3*7 4 1 = "111" also "33" to base 6 -> ( 7-1)
27 = 3^3= 3*9 8 3
33 = 3*11 10 3
35 = 5*7 6 5
39 = 3*13 12 3
45 = 3^2*5 8 5
51 = 3*17 16 3
55 = 5*11 10 5
57 = 3*19 7 1 also "33" to base 18
63 = 3^2*7 2 1 also "77" to base 8
65 = 5*13 12 5
69 = 3*23 22 3
75 = 3*5^2 14 5
77 = 7*11 10 7
81 = 3^4=3*27 26 3
85 = 5*17 4 1 also "55" to base 16
87 = 3*29 28 3
91 = 7*13 9 1
93 = 3*31 5 3
95 = 5*19 18 5
99 = 3^2*11 10 9
105 = 3*5*7 14 7
111 = 3*37 10 1 also "33" to base 36</pre>
I think, taking the factorization of the number leave the highest factor -1 > sqrt( number) as base and the rest as digit.Something to test.[[user:Horst.h|Horst.h]]
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