Recent developments in primality testing
Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more diff...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Pomerance, Carl [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
1981 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© Springer Science+Business Media, Inc. 1980 |
|---|
| Übergeordnetes Werk: |
Enthalten in: MD computing - Springer-Verlag, 1984, 3(1981), 3 vom: Sept., Seite 97-105 |
|---|---|
| Übergeordnetes Werk: |
volume:3 ; year:1981 ; number:3 ; month:09 ; pages:97-105 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF03022861 |
|---|
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OLC2091779733 |
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| 520 | |a Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! | ||
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10.1007/BF03022861 doi (DE-627)OLC2091779733 (DE-He213)BF03022861-p DE-627 ger DE-627 rakwb eng 004 610 VZ 44.00 bkl Pomerance, Carl verfasserin aut Recent developments in primality testing 1981 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 1980 Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! Primitive Root Primality Test Probabilistic Algorithm Chinese Remainder Theorem Decimal Digit Enthalten in MD computing Springer-Verlag, 1984 3(1981), 3 vom: Sept., Seite 97-105 (DE-627)129905909 (DE-600)312708-4 (DE-576)015285111 0343-6993 nnns volume:3 year:1981 number:3 month:09 pages:97-105 https://doi.org/10.1007/BF03022861 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 44.00 VZ AR 3 1981 3 09 97-105 |
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10.1007/BF03022861 doi (DE-627)OLC2091779733 (DE-He213)BF03022861-p DE-627 ger DE-627 rakwb eng 004 610 VZ 44.00 bkl Pomerance, Carl verfasserin aut Recent developments in primality testing 1981 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 1980 Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! Primitive Root Primality Test Probabilistic Algorithm Chinese Remainder Theorem Decimal Digit Enthalten in MD computing Springer-Verlag, 1984 3(1981), 3 vom: Sept., Seite 97-105 (DE-627)129905909 (DE-600)312708-4 (DE-576)015285111 0343-6993 nnns volume:3 year:1981 number:3 month:09 pages:97-105 https://doi.org/10.1007/BF03022861 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 44.00 VZ AR 3 1981 3 09 97-105 |
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10.1007/BF03022861 doi (DE-627)OLC2091779733 (DE-He213)BF03022861-p DE-627 ger DE-627 rakwb eng 004 610 VZ 44.00 bkl Pomerance, Carl verfasserin aut Recent developments in primality testing 1981 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 1980 Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! Primitive Root Primality Test Probabilistic Algorithm Chinese Remainder Theorem Decimal Digit Enthalten in MD computing Springer-Verlag, 1984 3(1981), 3 vom: Sept., Seite 97-105 (DE-627)129905909 (DE-600)312708-4 (DE-576)015285111 0343-6993 nnns volume:3 year:1981 number:3 month:09 pages:97-105 https://doi.org/10.1007/BF03022861 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 44.00 VZ AR 3 1981 3 09 97-105 |
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10.1007/BF03022861 doi (DE-627)OLC2091779733 (DE-He213)BF03022861-p DE-627 ger DE-627 rakwb eng 004 610 VZ 44.00 bkl Pomerance, Carl verfasserin aut Recent developments in primality testing 1981 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 1980 Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! Primitive Root Primality Test Probabilistic Algorithm Chinese Remainder Theorem Decimal Digit Enthalten in MD computing Springer-Verlag, 1984 3(1981), 3 vom: Sept., Seite 97-105 (DE-627)129905909 (DE-600)312708-4 (DE-576)015285111 0343-6993 nnns volume:3 year:1981 number:3 month:09 pages:97-105 https://doi.org/10.1007/BF03022861 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 44.00 VZ AR 3 1981 3 09 97-105 |
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10.1007/BF03022861 doi (DE-627)OLC2091779733 (DE-He213)BF03022861-p DE-627 ger DE-627 rakwb eng 004 610 VZ 44.00 bkl Pomerance, Carl verfasserin aut Recent developments in primality testing 1981 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 1980 Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! Primitive Root Primality Test Probabilistic Algorithm Chinese Remainder Theorem Decimal Digit Enthalten in MD computing Springer-Verlag, 1984 3(1981), 3 vom: Sept., Seite 97-105 (DE-627)129905909 (DE-600)312708-4 (DE-576)015285111 0343-6993 nnns volume:3 year:1981 number:3 month:09 pages:97-105 https://doi.org/10.1007/BF03022861 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 44.00 VZ AR 3 1981 3 09 97-105 |
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Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! © Springer Science+Business Media, Inc. 1980 |
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Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! © Springer Science+Business Media, Inc. 1980 |
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Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues! © Springer Science+Business Media, Inc. 1980 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2091779733</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230331071945.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230331s1981 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/BF03022861</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2091779733</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)BF03022861-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pomerance, Carl</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Recent developments in primality testing</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1981</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, Inc. 1980</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Conclusion Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. 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