Homework sagemath（6）.sagews

#6(a) when p=11
#(b) p=2,3,5,7,13,17,19,31,61,89

def M(p):
    M=2^p-1
    return M
for p in range(2,100):
    if (is_prime(p))and(is_prime(M(p))):
        print  M(p), 'is prime' ,p
    else:
        print M(p), 'is composite' ,p

3 is prime 2 7 is prime 3 15 is composite 4 31 is prime 5 63 is composite 6 127 is prime 7 255 is composite 8 511 is composite 9 1023 is composite 10 2047 is composite 11 4095 is composite 12 8191 is prime 13 16383 is composite 14 32767 is composite 15 65535 is composite 16 131071 is prime 17 262143 is composite 18 524287 is prime 19 1048575 is composite 20 2097151 is composite 21 4194303 is composite 22 8388607 is composite 23 16777215 is composite 24 33554431 is composite 25 67108863 is composite 26 134217727 is composite 27 268435455 is composite 28 536870911 is composite 29 1073741823 is composite 30 2147483647 is prime 31 4294967295 is composite 32 8589934591 is composite 33 17179869183 is composite 34 34359738367 is composite 35 68719476735 is composite 36 137438953471 is composite 37 274877906943 is composite 38 549755813887 is composite 39 1099511627775 is composite 40 2199023255551 is composite 41 4398046511103 is composite 42 8796093022207 is composite 43 17592186044415 is composite 44 35184372088831 is composite 45 70368744177663 is composite 46 140737488355327 is composite 47 281474976710655 is composite 48 562949953421311 is composite 49 1125899906842623 is composite 50 2251799813685247 is composite 51 4503599627370495 is composite 52 9007199254740991 is composite 53 18014398509481983 is composite 54 36028797018963967 is composite 55 72057594037927935 is composite 56 144115188075855871 is composite 57 288230376151711743 is composite 58 576460752303423487 is composite 59 1152921504606846975 is composite 60 2305843009213693951 is prime 61 4611686018427387903 is composite 62 9223372036854775807 is composite 63 18446744073709551615 is composite 64 36893488147419103231 is composite 65 73786976294838206463 is composite 66 147573952589676412927 is composite 67 295147905179352825855 is composite 68 590295810358705651711 is composite 69 1180591620717411303423 is composite 70 2361183241434822606847 is composite 71 4722366482869645213695 is composite 72 9444732965739290427391 is composite 73 18889465931478580854783 is composite 74 37778931862957161709567 is composite 75 75557863725914323419135 is composite 76 151115727451828646838271 is composite 77 302231454903657293676543 is composite 78 604462909807314587353087 is composite 79 1208925819614629174706175 is composite 80 2417851639229258349412351 is composite 81 4835703278458516698824703 is composite 82 9671406556917033397649407 is composite 83 19342813113834066795298815 is composite 84 38685626227668133590597631 is composite 85 77371252455336267181195263 is composite 86 154742504910672534362390527 is composite 87 309485009821345068724781055 is composite 88 618970019642690137449562111 is prime 89 1237940039285380274899124223 is composite 90 2475880078570760549798248447 is composite 91 4951760157141521099596496895 is composite 92 9903520314283042199192993791 is composite 93 19807040628566084398385987583 is composite 94 39614081257132168796771975167 is composite 95 79228162514264337593543950335 is composite 96 158456325028528675187087900671 is composite 97 316912650057057350374175801343 is composite 98 633825300114114700748351602687 is composite 99