Delicate prime
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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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