Timeline for At what times were people interested in prime numbers
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2012 at 15:15 | comment | added | John Stillwell | @Marty. I had my doubts about Bhaskara. Thanks for looking into this. | |
| Sep 11, 2012 at 7:26 | comment | added | Marty | Regarding Bhaskara I, I am just about ready to call it bunk. It is all over the internet, so it is popular bunk. I think that the bunk comes from misinterpreting the following: In Vol. 2, Ch II, p.59 of his "History of the Theory of Numbers", Dickson explains how both "Ibn al-Haitam (about 1000)" and "Bhascara (born, 1114 A.D.)" treated similar problems about finding a number which has given remainders when divided by 2,3,4,5,6. From the date, this would appear to be Bhaskara II. Al-Haitam's problem leads him to "Wilson's Theorem" context, but Wilson's theorem is absent from Bhaskara II. | |
| Sep 11, 2012 at 7:19 | comment | added | Marty | Ibn al-Haytham: "This being shown we say that this is a necessary property for any prime number, that is to say that for any prime number - which is the number that is a multiple only of the unit - if you multiply the numbers that precede each other in the way that we have introduced, and if we add one to the product, and if we divide the sum by each of the numbers before the prime number, there is one, and if it is divided by the prime number, nothing is left." | |
| Sep 11, 2012 at 7:15 | comment | added | Marty | Indeed, from Rashed's scholarly translation of Ibn al-Haytham, we find that Ibn al-Haytham knew "Wilson's theorem". An English translation can be found in "The Development of Arabic Mathematics: Between Arithmetic and Algebra" by the same Rashed. Since this large book is not all available on google books, I will provide an English translation of Rashed's French translation of the Arabic manuscript MSS Loth 734 (f. 121), which is the relevant section of al-Haytham's Oposcula. | |
| Sep 11, 2012 at 0:44 | comment | added | Marty | Thanks for the reference - I'll check it out. And I'll look through Bhaskara I for clues about primes as well. | |
| Sep 11, 2012 at 0:18 | comment | added | John Stillwell | @Marty: for Bhaskara I the only source I've seen is Wikipedia. However, for al-Haytham there is more scholarly support: Rashed, Roshdi Ibn al-Haytham et le théorème de Wilson. Arch. Hist. Exact Sci. 22 (1980), no. 4, 305–321. | |
| Sep 10, 2012 at 23:46 | comment | added | Marty | Who has claimed this? And based on what text of Bhaskara I? | |
| Sep 10, 2012 at 23:28 | history | answered | John Stillwell | CC BY-SA 3.0 |