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

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