# Euler's Phi Function of a Palindromic Prime

The Euler's Totient Function (phi function) Ο of a palindromic prime p is easy to compute.

Definition of Terms:

Euler's Phi Function- a number of positive integers less than or equal to n that are relatively prime to n.

Palindrome- a word, a phrase, a sequence, or a number that reads the same backward as forward.

Prime- a natural number greater than 1 that has no positive divisors other than 1 and itself.

Palindromic prime- a number that is simultaneously palindromic and prime.

Conjecture:

The phi function Ο of every palindromic prime p is equal to a given palindromic prime p minus 1.

In this conjecture, let n equals p.

Note: Palindromic prime, prime palindrome and palprime are synonymous. π

In symbols:

Ο(p)= p-1 (FORMULA) ππ¦

Example 1:

p= 929 (a palindromic prime)

Solution:

Use the formula.

Ο(929) = 929-1

= 928 βπ


Hence, Ο(929) = 928.

Example 2:

p= 13,331 (a palindromic prime)

Solution:

Use the formula.

 Ο(13331) = 13331-1

= 13,330 βπ


Hence, Ο(13331) = 13,330.

Now, you try! π

Exercises π

Compute the following:

1. Ο(10301)

2. Ο(1411141)

3. Ο(7619167)

4. Ο(7630367)

5. Ο(9989899)


Author: John Paul L. Hablado, LPT

     (c) April 11, 2017


References:

Kindly click each example link for the URL (Uniform Resource Locator), and some related theorems on Euler's Phi Function of a Palindromic Prime. β€

1. π example link

2. π example link

3. π example link

Note by John Paul Hablado
1Β year, 5Β months ago

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