1. 素数(Prime Number)
仅有1和它本身两个正因数的正整数,叫做素数,也叫质数。如:3,7,23。
设p为素数,若 p | ab,则p | a,或p | b。 如:
p = 2,a = 4,b = 7 —— 2 | 4×7 → 2 | 4
p = 7,a = 22,b = 21 —— 7 | 22×21 → 7 | 21
2. 合数(Composite Number)
含有三个或以上正因数的正整数,叫做合数。如:
4 = 1×4 = 2×2,
24 = 1×24 = 2×12 = 3×8 = 4×6
1既不是素数也不是合数,2是唯一的偶素数。
3. 100以内的素数
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, 43, 47, 53, 59, 61, 67, 69, 71, 73, 79, 83, 89, 97
4. 1000以内的素数
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, 43, 47, 53, 59, 61, 67, 69, 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
English:
SAT:
A rope is 13 feet long. How many ways can the rope be cut into more than one piece so that the length of each piece is a prime number?
A.4
B.5
C.6
D.7
E.8