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 add up all the smallest prime numbers until you reach or exceed your target number. How much is:
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 =
Right,
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 = 1060
Now, you are 60 OVER your target number. What is the smallest number of prime numbers that adds up to 60? Take those numbers out of your list, and you'll have the longest list of prime numbers that adds up to 1000.
I found six different answers that all had the largest number of different prime numbers that adds up to 1000. Here is one of them:
2+3+5+7+11+13+17+19+23+37+41+43+47+53+59+61+67+71+73+79+83+89+97 = 1000
Can you find the other five answers to this puzzle?
When you are ready, we can look at the fifth puzzle.
Find the largest number of different prime addends that add up to
1000
You may use both positive and negative prime numbers for this puzzle.