Academic Journal
Infinitely many composites
| Title: | Infinitely many composites |
|---|---|
| Authors: | Nick Lord, Des MacHale |
| Source: | The Mathematical Gazette. 108:20-26 |
| Publisher Information: | Cambridge University Press (CUP), 2024. |
| Publication Year: | 2024 |
| Subject Terms: | 0101 mathematics, 01 natural sciences |
| Description: | In number theory, we frequently ask if there are infinitely many prime numbers of a certain type. For example, if n is a natural number: (i)Are there infinitely many (Mersenne) primes of the form 2n − 1?(ii)Are there infinitely many primes of the form n2 + 1?These problems are often very difficult and many remain unsolved to this day, despite the efforts of many great mathematicians. However, we can sometimes comfort ourselves by asking if there are infinitely many composite numbers of a certain type. These questions are often (but not always) easier to answer. For example, echoing (i) above, we can ask if there are infinitely many composites of the form 2p − 1 with p a prime number but (to the best of our knowledge) this remains an unsolved problem. Of course, it must be the case that there are either infinitely many primes or infinitely many composites of the form 2p − 1 and it seems strange that we currently cannot decide on either of them. |
| Document Type: | Article |
| Language: | English |
| ISSN: | 2056-6328 0025-5572 |
| DOI: | 10.1017/mag.2024.4 |
| Rights: | Cambridge Core User Agreement |
| Accession Number: | edsair.doi...........976304484f05f65beca2073ca795c636 |
| Database: | OpenAIRE |
| ISSN: | 20566328 00255572 |
|---|---|
| DOI: | 10.1017/mag.2024.4 |