Can the bounds for the number of Carmichael numbers below $x$ be made more concrete?
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On the page:
https://en.wikipedia.org/wiki/Carmichael_number
at the part "distribution", lower and upper bounds for the number of Carmichael numbers below $x$ (denoted by $C(x)$) are given. Two questions about these bounds :
Which constant can be used for the upper bound ? Does $k_2=1$ do the job ?
What does "sufficiently large" mean for the lower bound ? For which $x$ does $large C(x)>x^frac{2}{7}$ hold ?
number-theory prime-factorization
edited Nov 22 at 13:54
Klangen
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asked Oct 13 '15 at 8:40
Peter
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up vote
1
down vote
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On the page:
https://en.wikipedia.org/wiki/Carmichael_number
at the part "distribution", lower and upper bounds for the number of Carmichael numbers below $x$ (denoted by $C(x)$) are given. Two questions about these bounds :
Which constant can be used for the upper bound ? Does $k_2=1$ do the job ?
What does "sufficiently large" mean for the lower bound ? For which $x$ does $large C(x)>x^frac{2}{7}$ hold ?
number-theory prime-factorization
edited Nov 22 at 13:54
Klangen
1,43711232
asked Oct 13 '15 at 8:40
Peter
46.4k1039125
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
On the page:
https://en.wikipedia.org/wiki/Carmichael_number
at the part "distribution", lower and upper bounds for the number of Carmichael numbers below $x$ (denoted by $C(x)$) are given. Two questions about these bounds :
Which constant can be used for the upper bound ? Does $k_2=1$ do the job ?
What does "sufficiently large" mean for the lower bound ? For which $x$ does $large C(x)>x^frac{2}{7}$ hold ?
number-theory prime-factorization
edited Nov 22 at 13:54
Klangen
1,43711232
asked Oct 13 '15 at 8:40
Peter
46.4k1039125
On the page:
https://en.wikipedia.org/wiki/Carmichael_number
at the part "distribution", lower and upper bounds for the number of Carmichael numbers below $x$ (denoted by $C(x)$) are given. Two questions about these bounds :
Which constant can be used for the upper bound ? Does $k_2=1$ do the job ?
What does "sufficiently large" mean for the lower bound ? For which $x$ does $large C(x)>x^frac{2}{7}$ hold ?
number-theory prime-factorization
number-theory prime-factorization
edited Nov 22 at 13:54
Klangen
1,43711232
asked Oct 13 '15 at 8:40
Peter
46.4k1039125
edited Nov 22 at 13:54
Klangen
1,43711232
asked Oct 13 '15 at 8:40
Peter
46.4k1039125
edited Nov 22 at 13:54
Klangen
1,43711232
edited Nov 22 at 13:54
Klangen
1,43711232
edited Nov 22 at 13:54
Klangen
1,43711232
1,43711232
asked Oct 13 '15 at 8:40
Peter
46.4k1039125
asked Oct 13 '15 at 8:40
Peter
46.4k1039125
asked Oct 13 '15 at 8:40
Peter
46.4k1039125
46.4k1039125
add a comment |
add a comment |
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