How to resolve the algorithm Primes: n*2^m+1 step by step in the PL/M programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Primes: n*2^m+1 step by step in the PL/M programming language
Table of Contents
Problem Statement
A050921 - Smallest prime of form n*2^m+1
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Primes: n*2^m+1 step by step in the PL/M programming language
Source code in the pl/m programming language
100H: /* FIND PRIMES OF THE FORM N * 2**M + 1 */
DECLARE FALSE LITERALLY '0';
DECLARE TRUE LITERALLY '0FFH';
/* CP/M SYSTEM CALL AND I/O ROUTINES */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
/* END SYSTEM CALL AND I/O ROUTINES */
/* SIEVE THE PRIMES TO 8000 */
DECLARE PRIME ( 8001 )BYTE;
DO;
DECLARE ( I, S ) ADDRESS;
PRIME( 0 ), PRIME( 1 ) = FALSE;
PRIME( 2 ) = TRUE;
DO I = 3 TO LAST( PRIME ) BY 2; PRIME( I ) = TRUE; END;
DO I = 4 TO LAST( PRIME ) BY 2; PRIME( I ) = FALSE; END;
DO I = 3 TO LAST( PRIME ) / 2 BY 2;
IF PRIME( I ) THEN DO;
DO S = I * I TO LAST( PRIME ) BY I + I; PRIME( S ) = FALSE; END;
END;
END;
END;
DECLARE MAX$M LITERALLY '14'; /* MAXIMUM M WE WILL CONSIDER */
/* FIND THE PRIMES */
DECLARE ( N, M, P, TWO$TO$M ) ADDRESS;
DECLARE NOT$FOUND BYTE;
DO N = 1 TO 45;
M = 0;
TWO$TO$M = 1;
P = 0;
NOT$FOUND = 1;
DO WHILE M <= MAX$M
AND ( NOT$FOUND := NOT PRIME( P := ( N * TWO$TO$M ) + 1 ) );
TWO$TO$M = TWO$TO$M + TWO$TO$M;
M = M + 1;
END;
CALL PR$CHAR( '(' );
IF N < 10 THEN CALL PR$CHAR( ' ' );
CALL PR$NUMBER( N );
IF NOT$FOUND THEN DO;
CALL PR$STRING( .' NOT FOUND$' );
END;
ELSE DO;
CALL PR$CHAR( ' ' );
CALL PR$NUMBER( M );
CALL PR$CHAR( ':' );
CALL PR$CHAR( ' ' );
IF P < 10 THEN CALL PR$CHAR( ' ' );
IF P < 100 THEN CALL PR$CHAR( ' ' );
IF P < 1000 THEN CALL PR$CHAR( ' ' );
CALL PR$NUMBER( P );
CALL PR$CHAR( ' ' );
CALL PR$CHAR( ' ' );
END;
CALL PR$CHAR( ')' );
IF N MOD 5 = 0 THEN CALL PR$NL;
END;
EOF
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