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CMSC201
Programming Project Two
Goldbach's Conjecture
Out: Tuesday 3/4/97
Due: Midnight Tuesday 3/18/97
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The Objective
The objective of this assignment is to give you some practice using for
loops, using #define for constants, writing functions and formatting output.
The Background
Christian Goldbach did important work in number theory, much of it in
correspondence with Euler. He is best remembered for his conjecture, made
in 1742 in a letter to Euler and still an open question, that every even
integer greater than 2 can be represented as the sum of two primes.
Some biographical information on Goldbach:
Born: March 18, 1690 in Konigsberg, Prussia (now Kaliningrad, Russia)
Died: November 20, 1764 in Moscow, Russia
In 1725 Goldbach became professor of mathematics and historian at St.
Petersburg. Then, in 1728, he went to Moscow as tutor to Tsar Peter II.
The Task
You are to test out Goldbach's conjecture on the even numbers between 200
and 400. The values 200 and 400 are the constants START and FINISH,
respectively. Your program should display the value and the two primes
that when added produce that value as their sum. (See the sample run below)
Your output should match the sample run shown below, exactly. There should
be 3 values and their primes displayed on each line of output.
You will be expected to use three functions, other than main, when writing
your program. Here are the function prototypes:
<![CDATA[
void PrintExplanation (void);
int Goldbach (int n);
bool IsPrime (int n);
]]>
Function Descriptions:
- PrintExplanation - should print a message to the user, explaining
what the program will do. Since this function returns nothing, it can also
be called a procedure.
- Goldbach - This function will take a positive even integer as its
single argument, n. One at a time, the function will test odd integers
between 3 and n to see if that odd integer is a prime number. (1 is not
prime, by definition) When a prime number is found, it should be subtracted
from n. The result needs to be tested to make sure that it is also a
prime number. If the result is also prime, you've found the two primes that
sum to the even number being checked. The function needs to return the first
of these two primes. Functions can only return one thing, in this case, one
integer. That integer happens to be the first prime number found that when
subtracted from the even number, n, results in a prime number.
- IsPrime - This function is a predicate function. It returns TRUE if the
number passed to it is a prime number and FALSE otherwise. A prime number
is a natural number (a positive integer) that is evenly divisible only by
itself and 1. By definition, 1 is not prime. So any integer less than or
equal to 1 is not prime. Also even positive integers, with the exception of 2,
are not prime.
The Sample Run
<![CDATA[
umbc9[1]% a.out
This program will demonstrate the truth of Goldbach's
conjecture for the even integers 200 through 400, inclusive.
The conjecture is that any even integer greater than 2 can
be expressed as the sum of two prime numbers.
200 = 3 + 197 202 = 3 + 199 204 = 5 + 199
206 = 7 + 199 208 = 11 + 197 210 = 11 + 199
212 = 13 + 199 214 = 3 + 211 216 = 5 + 211
218 = 7 + 211 220 = 23 + 197 222 = 11 + 211
224 = 13 + 211 226 = 3 + 223 228 = 5 + 223
230 = 3 + 227 232 = 3 + 229 234 = 5 + 229
236 = 3 + 233 238 = 5 + 233 240 = 7 + 233
242 = 3 + 239 244 = 3 + 241 246 = 5 + 241
248 = 7 + 241 250 = 11 + 239 252 = 11 + 241
254 = 3 + 251 256 = 5 + 251 258 = 7 + 251
260 = 3 + 257 262 = 5 + 257 264 = 7 + 257
266 = 3 + 263 268 = 5 + 263 270 = 7 + 263
272 = 3 + 269 274 = 3 + 271 276 = 5 + 271
278 = 7 + 271 280 = 3 + 277 282 = 5 + 277
284 = 3 + 281 286 = 3 + 283 288 = 5 + 283
290 = 7 + 283 292 = 11 + 281 294 = 11 + 283
296 = 3 + 293 298 = 5 + 293 300 = 7 + 293
302 = 19 + 283 304 = 11 + 293 306 = 13 + 293
308 = 31 + 277 310 = 3 + 307 312 = 5 + 307
314 = 3 + 311 316 = 3 + 313 318 = 5 + 313
320 = 3 + 317 322 = 5 + 317 324 = 7 + 317
326 = 13 + 313 328 = 11 + 317 330 = 13 + 317
332 = 19 + 313 334 = 3 + 331 336 = 5 + 331
338 = 7 + 331 340 = 3 + 337 342 = 5 + 337
344 = 7 + 337 346 = 29 + 317 348 = 11 + 337
350 = 3 + 347 352 = 3 + 349 354 = 5 + 349
356 = 3 + 353 358 = 5 + 353 360 = 7 + 353
362 = 3 + 359 364 = 5 + 359 366 = 7 + 359
368 = 19 + 349 370 = 3 + 367 372 = 5 + 367
374 = 7 + 367 376 = 3 + 373 378 = 5 + 373
380 = 7 + 373 382 = 3 + 379 384 = 5 + 379
386 = 3 + 383 388 = 5 + 383 390 = 7 + 383
392 = 3 + 389 394 = 5 + 389 396 = 7 + 389
398 = 19 + 379 400 = 3 + 397
umbc9[2]%
]]>
Submitting the Program
To submit the file you should use the command:
submit cs201 proj2 proj2.c
You can check your submission by using the command:
submitls cs201 proj2