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{{Merge to|Weakly prime number|discuss=Talk:Weakly prime number#Proposed merge of Delicate prime into Weakly prime number|date=April 2021}} |
{{Merge to|Weakly prime number|discuss=Talk:Weakly prime number#Proposed merge of Delicate prime into Weakly prime number|date=April 2021}} |
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A '''delicate prime''' or '''digitally delicate prime''' is a [[prime number]] |
A '''delicate prime''' or '''digitally delicate prime''' is a [[prime number]] which under some given [[radix]], modifies exactly one of its digits always results in a [[composite number]].<ref name=":1">{{Cite web|url=https://www.quantamagazine.org/mathematicians-find-a-new-class-of-digitally-delicate-primes-20210330/|title=Mathematicians Find a New Class of Digitally Delicate Primes|website=Quanta Magazine|access-date=2021-04-01}}</ref> In 2021, a new class of delicate primes was discovered.<ref name=":1" /> |
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In 2021, a new class of delicate primes was discovered.<ref name=":1" /> |
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== History == |
== History == |
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In 1978, [[Murray S. Klamkin]] posed the question of whether these numbers existed. [[Paul Erdős]] proved that there exists an infinite number of "delicate primes" under any base. [[Terence Tao]] proved in a 2011 paper that a positive proportion of primes is digitally delicate.<ref>{{cite arxiv|last=Tao|first=Terence|date=2010-04-18|title=A remark on primality testing and decimal expansions|class=math.NT|eprint=0802.3361}}</ref> Positive proportion here means as the primes get bigger, the distance between the delicate primes will be quite similar, thus not scarce.<ref name=":1" /> |
In 1978, [[Murray S. Klamkin]] posed the question of whether these numbers existed.<ref>{{Cite web|last=Nadis|first=Steve|date=2021-03-30|title=Mathematicians Find a New Class of Digitally Delicate Primes|url=https://www.quantamagazine.org/mathematicians-find-a-new-class-of-digitally-delicate-primes-20210330/|access-date=2021-05-25|website=Quanta Magazine|language=en}}</ref> [[Paul Erdős]] proved that there exists an infinite number of "delicate primes" under any base.<ref>{{Cite web|title=https://twitter.com/quantamagazine/status/1376906089938161666|url=https://twitter.com/quantamagazine/status/1376906089938161666|access-date=2021-05-25|website=Twitter|language=en}}</ref> [[Terence Tao]] proved in a 2011 paper that a positive proportion of primes is digitally delicate.<ref>{{cite arxiv|last=Tao|first=Terence|date=2010-04-18|title=A remark on primality testing and decimal expansions|class=math.NT|eprint=0802.3361}}</ref> Positive proportion here means as the primes get bigger, the distance between the delicate primes will be quite similar, thus not scarce.<ref name=":1" /> |
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In 2021, [[Michael Filaseta]] of [[University of South Carolina|the University of South Carolina]] tried to find a delicate prime number such that you add an infinite amount of leading zeros to the prime number and if you change any one of those zeros, it becomes non-prime. He called these numbers, "widely digitally delicate". He with a student of his showed in the paper that there exists an infinite number of these numbers, although they could not produce a single example of this, having looked through 1 to 1 billion. They also proved that a positive proportion of primes are widely digitally delicate.<ref name=":1" /> |
In 2021, [[Michael Filaseta]] of [[University of South Carolina|the University of South Carolina]] tried to find a delicate prime number such that you add an infinite amount of leading zeros to the prime number and if you change any one of those zeros, it becomes non-prime. He called these numbers, "widely digitally delicate".<ref>{{Cite journal|last=Filaseta|first=Michael|last2=Juillerat|first2=Jacob|date=2021-01-21|title=Consecutive primes which are widely digitally delicate|url=http://arxiv.org/abs/2101.08898|journal=arXiv:2101.08898 [math]}}</ref> He with a student of his showed in the paper that there exists an infinite number of these numbers, although they could not produce a single example of this, having looked through 1 to 1 billion. They also proved that a positive proportion of primes are widely digitally delicate.<ref name=":1" /> |
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==References== |
==References== |
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Revision as of 08:16, 25 May 2021
 | It has been suggested that this article be merged into Weakly prime number. (Discuss) Proposed since April 2021. |
A delicate prime or digitally delicate prime is a prime number which under some given radix, modifies exactly one of its digits always results in a composite number.[1] In 2021, a new class of delicate primes was discovered.[1]
History
In 1978, Murray S. Klamkin posed the question of whether these numbers existed.[2] Paul Erdős proved that there exists an infinite number of "delicate primes" under any base.[3] Terence Tao proved in a 2011 paper that a positive proportion of primes is digitally delicate.[4] Positive proportion here means as the primes get bigger, the distance between the delicate primes will be quite similar, thus not scarce.[1]
In 2021, Michael Filaseta of the University of South Carolina tried to find a delicate prime number such that you add an infinite amount of leading zeros to the prime number and if you change any one of those zeros, it becomes non-prime. He called these numbers, "widely digitally delicate".[5] He with a student of his showed in the paper that there exists an infinite number of these numbers, although they could not produce a single example of this, having looked through 1 to 1 billion. They also proved that a positive proportion of primes are widely digitally delicate.[1]
References
- ^ a b c d "Mathematicians Find a New Class of Digitally Delicate Primes". Quanta Magazine. Retrieved 2021-04-01.
- ^ Nadis, Steve (2021-03-30). "Mathematicians Find a New Class of Digitally Delicate Primes". Quanta Magazine. Retrieved 2021-05-25.
- ^ "https://twitter.com/quantamagazine/status/1376906089938161666". Twitter. Retrieved 2021-05-25.
{{cite web}}: External link in|title= - ^ Tao, Terence (2010-04-18). "A remark on primality testing and decimal expansions". arXiv:0802.3361 [math.NT].
- ^ Filaseta, Michael; Juillerat, Jacob (2021-01-21). "Consecutive primes which are widely digitally delicate". arXiv:2101.08898 [math].
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