Fifth Prime Number Puzzle

  

Find the largest number of different prime addends that add up to 1000

Remember, you are also allowed to use negative prime numbers for this particular puzzle.
This particular strategy is one that your teachers may not think of if they assign this problem.

Just in case you need them, here is a list of all the prime numbers up to 1000. Try to find your best answer before you scroll down for my answer.

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

Scroll down for my answer.

What I suggest you do is first decide what prime number is going to be the largest one that will be in your answer. Since I listed the prime numbers up to 997, I'm going to use 997 as my largest number.

• We are going to keep a running total as we work.
• Write down the largest prime number that you are going to use and your running total so far.
  • 997 = 997
• Now, you have to decide if your next smaller prime number will be positive or negative
  • If your running total is greater than your target number, use the negative
  • If your running total is less than or equal to the target, use the positve
• 997 is less than 1000, so use the next lower positive prime number, 991
  • 997 + 991 = 1988
• 1988 is greater than 1000, so use the negative prime number 983
  • 997 + 991 + -983 = 1005
• 1005 is greater than 1000, so we again use a negative prime number
  • 997 + 991 + -983 + -977 = ???
• Keep doing this until you get close to your target number and you are down to the last few prime numbers in your list.

Congratulations. You have graduated from Prime Numbers 101, 102, 103, 104, 105.