INTEGER N1
1 WRITE(5,2) ' Enter a number: '
2 FORMAT( A,$ )
READ(5,3) N1
3 FORMAT( I )
CALL FACTOR( N1 )
GOTO 1
END
SUBROUTINE FACTOR ( N )
C Factor N
C Test for factors of 2,3,5,... using NEXTPRIME function to get next prime.
INTEGER N, NUMBER, PRIME
NUMBER = N
PRIME = 2 !Start with 2
10 CONTINUE
IF (NUMBER .EQ. 0) RETURN
IF ( MOD(NUMBER,PRIME) .EQ. 0 ) THEN !prime is a factor
WRITE(6,1) PRIME
NUMBER = NUMBER / PRIME
IF (NUMBER .EQ. 1) RETURN
ELSE
PRIME = NEXTPRIME(PRIME+1) !Else test the next prime
ENDIF
GOTO 10
1 FORMAT(1X,'FACTOR ',I)
END
INTEGER FUNCTION NEXTPRIME( N )
C Return next prime number .GE. N
C
C For N .GE. 1,018,801 returns next number relatively prime to all
C primes below 1009.
C Note: 1009 is next prime after 997, and 1,018,801 = 1009^2.
C The database may be extended if larger primes are desired.
C
C Outline:
C 1. If number .LE. 3 then return number.
C Number is prime, zero, or negative.
C 2. If number between 4 and 997 then search PRIME array
C for next prime .GE. number. An approximating polynomial
C is used to give us a good initial guess for the index I
C so that PRIME(I) is very close to the prime we seek.
C The approximating polynomial is:
C
C I = -0.3034277E-04*X^2 + 0.1918667*X + 8.0918350
C
C The optimum coefficients for this polynomial were obtained
C using the OPTIMIZE program in the [.OPTIMIZE] directory.
C Look there for further details. Thus, this function is right
C on the money 452 times, is low by one 224 times, is low by two
C 40 times, and is low by three 1 time. It's high by one 185
C times, high by two 68 times, high by three 12 times, high by
C four 7 times, high by five 4 times, and high by 6 one time.
C
C 3. Else number is greater than 997. Do normal search for next prime.
C 3a. Increment NUMBER to an odd number. Since even numbers are
C not prime we skip over even numbers.
C 3b. Test if NUMBER is evenly divisible by any prime in the
C PRIME array less than SQRT(NUMBER).
C If NUMBER MOD PRIME(I) = 0, then NUMBER is not prime.
INTEGER N, NUMBER
INTEGER NUMPRIMES
PARAMETER (NUMPRIMES = 168)
INTEGER PRIME(NUMPRIMES)
DATA PRIME /
* 2, 3, 5, 7, 11, 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, 127, 131, 137, 139, 149, 151, 157, 163, 167,
* 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239,
* 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313,
* 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
* 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
* 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569,
* 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643,
* 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
* 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823,
* 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
* 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 /
NUMBER = N
IF (NUMBER .LE. 3) THEN !if number .le. 3 then return number
NEXTPRIME = NUMBER
RETURN
ENDIF
IF (NUMBER .LE. 997) THEN !just search thru PRIME array
I = (-0.3034277E-04*NUMBER + 0.1918667)*NUMBER + 8.0918350 !(see comments above)
I = MIN(I,NUMPRIMES) !don't let I go above 997
DO WHILE (PRIME(I) .LT. NUMBER) !Search upward for first prime greater than NUMBER
I = I + 1
ENDDO
DO WHILE (PRIME(I) .GE. NUMBER) !Search downward for first prime less than NUMBER,
I = I - 1
ENDDO
NEXTPRIME = PRIME(I+1) !then take next prime.
RETURN
ELSE !Else normal search for next prime
IF ( MOD(NUMBER,2) .EQ. 0 ) NUMBER = NUMBER + 1 !rule out even numbers. They are not prime
I = 2 !start with second prime since we only test odd numbers.
DO WHILE ( PRIME(I)*PRIME(I) .LE. NUMBER ) !test for all primes .LE. SQRT(NUMBER)
IF ( MOD(NUMBER,PRIME(I)) .EQ. 0 ) THEN !it's not prime
NUMBER = NUMBER + 2 !even numbers aren't prime
I = 2 !start over again with new number
ELSE
I = I + 1 !test with next prime
IF ( I .GT. NUMPRIMES) GOTO 10 !exit loop. NUMBER is relatively prime to first 168 primes.
ENDIF
ENDDO
10 NEXTPRIME = NUMBER
RETURN
ENDIF
END
