HP Prime and TI-84 Plus: Sieve of Eratosthenes

HP Prime and TI-84 Plus: Sieve of Eratosthenes

Introduction

The program SIEVEMIN shows a miniature version of the famous Sieve of Eratosthenes.  The Sieve of Eratosthenes is a Greek algorithm that determines prime numbers from 2 to N through eliminating multiplies.

Algorithm:

1.  List all integers from 1 to n.  Of course, you choose what n is. 

2.   1 is not a prime number, hence eliminate 1. 

3.  Start with 2.  Eliminate multiple of 2, but not 2 itself.

4.  Then do step 3, but with multiples of 3, but not 3 itself.

5.  Then do step 5, but with multiples of 5, but not 5 itself. 

6.  Continue on with the next available number until there are no multiples remaining.  At the end, you have all the prime numbers from 1 to n.

Most sieves will demonstrate the algorithm from 1 to 100.  However, to fit the calculator screens, SIEVEMIN finds all the prime numbers from 1 to 49. 

HP Prime Program: SIEVEMIN 

sub1(); // subroutine

EXPORT SIEVEMIN()
BEGIN
// 2018-12-18 EWS
// Mini Sieve
HFormat:=0; // standard
PRINT();
PRINT("Mini Sieve");
WAIT(1);
LOCAL M0,T,R,C,K;
T:=1;
M0:=MAKEMAT(0,7,7);

FOR R FROM 1 TO 7 DO
FOR C FROM 1 TO 7 DO
M0(R,C):=T;
T:=1+T;
END;
END;

sub1(M0);

M0(1,1):=0;
FOR K FROM 2 TO 7 DO
FOR R FROM 1 TO 7 DO
FOR C FROM 1 TO 7 DO
IF FP(M0(R,C)/K)==0 AND 
M0(R,C)>K THEN
M0(R,C):=0;
sub1(M0);
END;
END;
END;
END;

// end of program

END;

sub1(M1)
BEGIN
PRINT();
LOCAL I;
FOR I FROM 1 TO 7 DO
PRINT(row(M1,I));
END;
WAIT(0.5);
END;

TI-84 Plus CE Program:  SIEVEMIN

"2018-12-11 EWS"
Disp "MINI SIEVE OF","ERATOSHENES","TI-84 PLUS CE"
Float
Wait 1
{7,7}→dim([J])
1→T
For(R,1,7)
For(C,1,7)
T→[J](R,C)
1+T→T
End
End
ClrHome
Disp [J]
Wait 1

0→[J](1,1)
For(K,2,7)
For(R,1,7)
For(C,1,7)
If fPart([J](R,C)/K)=0 and [J](R,C)>K
Then
0→[J](R,C)
ClrHome
Disp [J]
Wait .5
End
End
End
End

Eddie

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