HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 284
Isprime?b3, Isprime?, Functions, Integer
UPC - 882780045217
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hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM 16-10 Show that the whole numbers k such that: 10n ≤ k < 10n + 1 have (n + 1) digits in decimal notation. We have: 10n < 3 ⋅ 10n < an < 4 ⋅ 10n < 10n + 1 10n < bn < 2 ⋅ 10n < 10n + 1 10n < 2 ⋅ 10n < cn < 3 ⋅ 10n < 10n + 1 so an,bn,cn have (n + 1) digits in decimal notation. Moreover, dn = 10n - 1 is divisible by 9, since its decimal notation can only end in 9. We also have: an = 3 ⋅ 10n + dn and cn = 3 ⋅ 10n - dn so an and cn are both divisible by 3. Let's consider whether B(3) is a prime number. Type ISPRIME?(B(3)) and press . The result is 1, which means true. In other words, B(3) is a prime. Note: ISPRIME? is not available from a CAS soft menu, but you can select it from from CAS FUNCTIONS menu while you are in the Equation Writer by pressing , choosing the INTEGER menu, and scrolling to the ISPRIME? function. To prove that b3 = 1999 is a prime number, it is necessary to show that 1999 is not divisible by any of the prime numbers less than or equal to 1999 . As 1999 < 2025 = 452 , that means testing the divisibility of 1999 by n = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41. 1999 is not divisible by any of these numbers, so we can conclude that 1999 is prime. Step-by-Step Examples