Rexx is a language that can help you to solve these exercices with the instruction numeric digits.
If q is prime and (2^q)-1 is prime, then M(q) = ( 2^(q-1) ) * ( (2^q)-1 )
is called a perfect number; Among the following numbers, which q does NOT
give a perfect number ?
2 3 5 7 11 13 17 19 31 61
89 107 127 521 607 1279 2203 2281 3217 4253
4423 9689 9941 11213 19937 21701 23209 44497 86243 110503
132049 216091
A prime number n of the form (2^q)-1 is prime, is called a Mersenne number and q
is said to be its generator. All Mersenne numbers give a perfect number.
Be careful : the last number has 65050 digits !
Exercise 2 :
I got this file with OCR (where are the mistakes ?)
Nombres premiers inférieurs à 1200
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
353 359 397 373 379 383 389 397 401 409 419 421 431 433
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
1009 1013 1019 1021 1031 1033 l039 1049 1051 1061 1063 1069 1087 1091
1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193
Nombres premiers au voisinage de 4096
3877 3881 3889 3907 3911 3911 3919 3923 3929 3931 3943 3947 3967 3989
4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093
4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219
4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337
Nombres premiers au voisinage de 2^32 = 4 294 967 296
4294966553 4294966583 4294966591 4294966619 4294966639 4294966651 4294966657
4294966661 4294966667 4294966769 4294966813 4294966829 4294966877 4294966909
4294966927 4294966943 4294966981 4294966997 4294967029 4294967087 4294967111
4294967143 4294967161 4294967189 4294967197 4294967231 4294967279 4294967291
4294967311 4294967357 4294967371 4294967377 4294967387 4294967389 4294967459
4294967477 4294967497 4294967513 4294967539 4294967543 4294967549 4294967561
4294967563 4294967569 4294967597 4294967627 4294967639 4294967653 4294967681
4294967687 4294967701 4294967723 4294967î59 4294967779 4294967783 4294967791