Checking if a number is a prime number
Calculator: TI-34 II.
Checking if a multi-digit whole number is prime is computationally tedious. Here we show how to check whether or not a number greater than 113 but smaller than 12770 = 1132 + 1 is prime. Every composite number n in this range has a prime factor smaller than or equal to 113. We will find whether n has a prime divisor ≤ 113 by computing its greatest common divisor with the product of all these primes.
Here is the list of all the primes up to 113:
2 3 5 7 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113
Program.
OP1=gcd(Ans,A)gcd(Ans,B)gcd(Ans,C)gcd(Ans,D)gcd(Ans,E) [=][=]
2*3*5*7*11*13*17*19*23*29→A 6469693230.
31*37*41*43*47*53→B 5037203051.
59*61*67*71*73→C 1249792339.
79*83*89*97*101→D 5717264681.
103*107*109*113→E 135745657.
Now in order to check whether a number n is prime, press
n [=]
OP1
If the display is 1, n is prime. Otherwise, the display shows a factor f of n (possibly equal to n) which is a product of prime numbers smaller than 113.
Task.
3 5 7 is the only triplet of odd primes.
But there are many twins:
|
5 |
7 |
|
11 |
13 |
|
17 |
19 |
|
29 |
31 |
|
41 |
43 |
|
71 |
73 |
|
101 |
103 |
|
107 |
109 |
Can you find more of them?
In order to look for a pair of twins, define OP2=Ans(Ans+2)
and then press n OP2 OP1
The answer is 1 when both n and n+2 are prime, providing that both numbers are in the range 113 < n < n+2 < 12770.