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Prime Residue Class of Uniform Charges on the Integers
There is a probability charge on the power set of the integers that gives probability 1 / p to every residue class modulo a prime p . There exists such a charge that gives probability w to the set of prime numbers iff w ∈ [ 0 , 1 / 2 ] . Similarly, there is such a charge that gives probability x to...
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| Published in: | Journal of theoretical probability 2020-03, Vol.33 (1), p.340-360 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c316t-5710bdf436dc3048a8ebe50917087e4bbdd51f64335d68ffcea771c2143e00da3 |
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| cites | cdi_FETCH-LOGICAL-c316t-5710bdf436dc3048a8ebe50917087e4bbdd51f64335d68ffcea771c2143e00da3 |
| container_end_page | 360 |
| container_issue | 1 |
| container_start_page | 340 |
| container_title | Journal of theoretical probability |
| container_volume | 33 |
| creator | Spece, Michael Kadane, Joseph B. |
| description | There is a probability charge on the power set of the integers that gives probability 1 /
p
to every residue class modulo a prime
p
. There exists such a charge that gives probability
w
to the set of prime numbers iff
w
∈
[
0
,
1
/
2
]
. Similarly, there is such a charge that gives probability
x
to a residue class modulo
c
, where
c
is composite, iff
x
∈
[
0
,
1
/
y
]
, where
y
is the largest prime factor of
c
. |
| doi_str_mv | 10.1007/s10959-018-0860-y |
| format | article |
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p
to every residue class modulo a prime
p
. There exists such a charge that gives probability
w
to the set of prime numbers iff
w
∈
[
0
,
1
/
2
]
. Similarly, there is such a charge that gives probability
x
to a residue class modulo
c
, where
c
is composite, iff
x
∈
[
0
,
1
/
y
]
, where
y
is the largest prime factor of
c
.</description><identifier>ISSN: 0894-9840</identifier><identifier>EISSN: 1572-9230</identifier><identifier>DOI: 10.1007/s10959-018-0860-y</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Integers ; Mathematics ; Mathematics and Statistics ; Prime numbers ; Probability Theory and Stochastic Processes ; Statistics</subject><ispartof>Journal of theoretical probability, 2020-03, Vol.33 (1), p.340-360</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>2018© Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-5710bdf436dc3048a8ebe50917087e4bbdd51f64335d68ffcea771c2143e00da3</citedby><cites>FETCH-LOGICAL-c316t-5710bdf436dc3048a8ebe50917087e4bbdd51f64335d68ffcea771c2143e00da3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Spece, Michael</creatorcontrib><creatorcontrib>Kadane, Joseph B.</creatorcontrib><title>Prime Residue Class of Uniform Charges on the Integers</title><title>Journal of theoretical probability</title><addtitle>J Theor Probab</addtitle><description>There is a probability charge on the power set of the integers that gives probability 1 /
p
to every residue class modulo a prime
p
. There exists such a charge that gives probability
w
to the set of prime numbers iff
w
∈
[
0
,
1
/
2
]
. Similarly, there is such a charge that gives probability
x
to a residue class modulo
c
, where
c
is composite, iff
x
∈
[
0
,
1
/
y
]
, where
y
is the largest prime factor of
c
.</description><subject>Integers</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Prime numbers</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Statistics</subject><issn>0894-9840</issn><issn>1572-9230</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kE9LAzEUxIMoWKsfwNuC5-jLJtkkR1nUFgqK2HPIbl76h3a3JttDv70pK3jy9GCYmcf8CLln8MgA1FNiYKShwDQFXQE9XZAJk6qkpuRwSSagjaBGC7gmNyltAcAYgAmpPuJmj8Unpo0_YlHvXEpFH4pltwl93Bf12sUVZqkrhjUW827AFcZ0S66C2yW8-71Tsnx9-apndPH-Nq-fF7TlrBqoVAwaHwSvfMtBaKexQQmGKdAKRdN4L1moBOfSVzqEFp1SrC2Z4AjgHZ-Sh7H3EPvvI6bBbvtj7PJLW3IplNJCsuxio6uNfUoRgz3kVS6eLAN7xmNHPDbjsWc89pQz5ZhJ2dvlTX_N_4d-AG_0ZuQ</recordid><startdate>20200301</startdate><enddate>20200301</enddate><creator>Spece, Michael</creator><creator>Kadane, Joseph B.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20200301</creationdate><title>Prime Residue Class of Uniform Charges on the Integers</title><author>Spece, Michael ; Kadane, Joseph B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-5710bdf436dc3048a8ebe50917087e4bbdd51f64335d68ffcea771c2143e00da3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Integers</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Prime numbers</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Spece, Michael</creatorcontrib><creatorcontrib>Kadane, Joseph B.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of theoretical probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Spece, Michael</au><au>Kadane, Joseph B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Prime Residue Class of Uniform Charges on the Integers</atitle><jtitle>Journal of theoretical probability</jtitle><stitle>J Theor Probab</stitle><date>2020-03-01</date><risdate>2020</risdate><volume>33</volume><issue>1</issue><spage>340</spage><epage>360</epage><pages>340-360</pages><issn>0894-9840</issn><eissn>1572-9230</eissn><abstract>There is a probability charge on the power set of the integers that gives probability 1 /
p
to every residue class modulo a prime
p
. There exists such a charge that gives probability
w
to the set of prime numbers iff
w
∈
[
0
,
1
/
2
]
. Similarly, there is such a charge that gives probability
x
to a residue class modulo
c
, where
c
is composite, iff
x
∈
[
0
,
1
/
y
]
, where
y
is the largest prime factor of
c
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10959-018-0860-y</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0894-9840 |
| ispartof | Journal of theoretical probability, 2020-03, Vol.33 (1), p.340-360 |
| issn | 0894-9840 1572-9230 |
| language | eng |
| recordid | cdi_proquest_journals_2354778451 |
| source | Springer Link |
| subjects | Integers Mathematics Mathematics and Statistics Prime numbers Probability Theory and Stochastic Processes Statistics |
| title | Prime Residue Class of Uniform Charges on the Integers |
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