\u039f Martin Mersenne (\u039c\u03b5\u03c1\u03c3\u03ad\u03bd) (1588-1648) \u03ae\u03c4\u03b1\u03bd \u03ad\u03bd\u03b1\u03c2 \u0393\u03ac\u03bb\u03bb\u03bf\u03c2 \u03ba\u03b1\u03bb\u03cc\u03b3\u03b5\u03c1\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03c4\u03b1 \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd\u03c4\u03ac \u03c4\u03bf\u03c5 \u03b4\u03b5\u03bd \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03bd \u03bc\u03cc\u03bd\u03bf \u03c3\u03b5 \u03b8\u03c1\u03b7\u03c3\u03ba\u03b5\u03c5\u03c4\u03b9\u03ba\u03ac \u03b8\u03ad\u03bc\u03b1\u03c4\u03b1!
\n\u0389\u03c4\u03b1\u03bd \u03b8\u03b5\u03bf\u03bb\u03cc\u03b3\u03bf\u03c2, \u03c6\u03b9\u03bb\u03cc\u03c3\u03bf\u03c6\u03bf\u03c2, \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03ba\u03b1\u03b9 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2.
\n\u039b\u03ac\u03c4\u03c1\u03b5\u03c5\u03b5 \u03c4\u03b7 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 \u03ae\u03c4\u03b1\u03bd \u03bf \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03b1\u03bd\u03ad\u03c0\u03c4\u03c5\u03be\u03b5 \u03bc\u03b9\u03b1 \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03bc\u03ad\u03bd\u03b7 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03b1\u03c1\u03bc\u03bf\u03bd\u03af\u03b1\u03c2, \u03ad\u03c4\u03c3\u03b9 \u03c3\u03c5\u03c7\u03bd\u03ac \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03c9\u03c2 \u03bf \u00ab\u03c0\u03b1\u03c4\u03ad\u03c1\u03b1\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03ba\u03bf\u03c5\u03c3\u03c4\u03b9\u03ba\u03ae\u03c2\u00bb<\/p>\n
\u0388\u03bd\u03b1\u03c2 \u03c4\u03bf\u03bc\u03ad\u03b1\u03c2 \u03c4\u03c9\u03bd \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03b5\u03c1\u03cc\u03bd\u03c4\u03c9\u03bd \u03c4\u03bf\u03c5 \u03ae\u03c4\u03b1\u03bd \u03ba\u03b1\u03b9 \u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac. \u0391\u03bb\u03bb\u03b7\u03bb\u03bf\u03b3\u03c1\u03b1\u03c6\u03bf\u03cd\u03c3\u03b5 \u03c0\u03bf\u03bb\u03cd \u03c3\u03c5\u03c7\u03bd\u03ac \u03bc\u03b5 \u03c4\u03bf \u03a6\u03b5\u03c1\u03bc\u03ac (Fermat) \u03ba\u03b1\u03b9 \u03ae\u03c4\u03b1\u03bd \u03b1\u03c5\u03c4\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03b4\u03b7\u03bc\u03bf\u03c3\u03b9\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b5 \u03c0\u03bf\u03bb\u03bb\u03bf\u03cd\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03b9\u03c3\u03c7\u03c5\u03c1\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2 \u03c4\u03bf\u03c5 \u03ba\u03b1\u03b8\u03ce\u03c2 \u03ba\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u0393\u03b1\u03bb\u03b9\u03bb\u03b1\u03af\u03bf, \u03a0\u03b1\u03c3\u03ba\u03ac\u03bb \u03ba\u03b1\u03b9 \u03c0\u03bf\u03bb\u03bb\u03bf\u03cd\u03c2 \u03b1\u03ba\u03cc\u03bc\u03b1 \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03c0\u03bf\u03c7\u03ae\u03c2 \u03c4\u03bf\u03c5.<\/p>\n
\u039f \u039c\u03b5\u03c1\u03c3\u03ad\u03bd \u03ad\u03b4\u03b5\u03b9\u03be\u03b5 \u03c0\u03bf\u03bb\u03cd \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd \u03b3\u03b9\u03b1 \u03c4\u03bf\u03c5\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 (\u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03af\u03c4\u03b1\u03b9 \u03bc\u03cc\u03bd\u03bf \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03bf\u03bd \u03b5\u03b1\u03c5\u03c4\u03cc \u03c4\u03bf\u03c5) \u03ba\u03b1\u03b9 \u03ad\u03c6\u03c4\u03b9\u03b1\u03be\u03b5 \u03ad\u03bd\u03b1 \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc \u03bc\u03b5 \u03c4\u03bf\u03bd \u03bf\u03c0\u03bf\u03af\u03bf \u03c0\u03c1\u03bf\u03c3\u03c0\u03b1\u03b8\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03c4\u03bf\u03c5\u03c2 \u03c0\u03b1\u03c1\u03ac\u03b3\u03b5\u03b9.<\/p>\n
\u0397 \u03b9\u03b4\u03ad\u03b1 \u03c4\u03bf\u03c5 \u039c\u03b5\u03c1\u03c3\u03ad\u03bd \u03ae\u03c4\u03b1\u03bd \u03c0\u03ac\u03c1\u03b1 \u03c0\u03bf\u03bb\u03cd \u03b1\u03c0\u03bb\u03ae. \u03a0\u03c1\u03bf\u03c3\u03c0\u03b1\u03b8\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03c6\u03c4\u03b9\u03ac\u03be\u03b5\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03bf 2 \u03c0\u03bf\u03bb\u03bb\u03ad\u03c2 \u03c6\u03bf\u03c1\u03ad\u03c2 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b5\u03b1\u03c5\u03c4\u03cc \u03c4\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03b1\u03c6\u03b1\u03b9\u03c1\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1 (2^N\u20131) \u03b3\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 2x2x2x2x2 \u2013 1 = 31 \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2.
\n\u0392\u03ad\u03b2\u03b1\u03b9\u03b1 \u03bf \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b1\u03c5\u03c4\u03cc\u03c2 \u03b4\u03b5\u03bd \u03ad\u03b4\u03b9\u03bd\u03b5 \u03c0\u03ac\u03bd\u03c4\u03b1 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2, \u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2x2x2x2 \u2013 1 = 15 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2.
\n\u0393\u03c1\u03ae\u03b3\u03bf\u03c1\u03b1 \u03ba\u03b1\u03c4\u03ac\u03bb\u03b1\u03b2\u03b5 \u03c0\u03c9\u03c2 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf 2^N\u20131 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03ad\u03c0\u03c1\u03b5\u03c0\u03b5 \u03ba\u03b1\u03b9 \u03c4\u03bf N \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2. \u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2^4\u20131 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c6\u03bf\u03cd \u03c4\u03bf 4 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 (\u03cc\u03c7\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2).
\n\u0397 \u03ba\u03b1\u03c4\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03ad\u03b3\u03b9\u03bd\u03b5 \u03b1\u03ba\u03cc\u03bc\u03b1 \u03c0\u03b9\u03bf \u03c0\u03bf\u03bb\u03cd\u03c0\u03bb\u03bf\u03ba\u03b7 \u03cc\u03c4\u03b1\u03bd \u03b1\u03bd\u03c4\u03b9\u03bb\u03ae\u03c6\u03b8\u03b7\u03ba\u03b5 \u03cc\u03c4\u03b9 \u03b1\u03ba\u03cc\u03bc\u03b1 \u03ba\u03b1\u03b9 \u03b1\u03bd \u03bf \u03b5\u03ba\u03b8\u03ad\u03c4\u03b7\u03c2 N \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2, \u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2^N\u20131 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c5\u03c0\u03bf\u03c7\u03c1\u03b5\u03c9\u03c4\u03b9\u03ba\u03ac \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2. \u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2^11\u20131=2047=23\u221789 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03bf\u03c2 \u03c0\u03b1\u03c1\u03cc\u03bb\u03bf \u03c0\u03bf\u03c5 \u03c4\u03bf 11 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2.<\/p>\n
\u039c\u03ad\u03c3\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7 \u03b1\u03c5\u03c4\u03ce\u03bd \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03bf \u039c\u03b5\u03c1\u03c3\u03ad\u03bd \u03ba\u03ac\u03bd\u03b5\u03b9 \u03bc\u03af\u03b1 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b5\u03c8\u03b7:
\n\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2^N\u20131 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03bf\u03c5 N 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257<\/p>\n
\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2^257\u20131 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03cc\u03c3\u03bf \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03c0\u03ac\u03c1\u03b1 \u03c0\u03bf\u03bb\u03cd \u03b4\u03cd\u03c3\u03ba\u03bf\u03bb\u03b1 \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf\u03c2 \u03b8\u03b1 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03b1\u03bc\u03c6\u03b9\u03c3\u03b2\u03b7\u03c4\u03ae\u03c3\u03b5\u03b9 \u03c4\u03b7\u03bd \u03c0\u03c1\u03cc\u03b2\u03bb\u03b5\u03c8\u03ae \u03c4\u03bf\u03c5.<\/p>\n
\u03a4\u03bf 1857 \u03bf \u0393\u03ac\u03bb\u03bb\u03bf\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 Edouard Lucas (1842 \u2013 1891) \u03c3\u03b5 \u03b7\u03bb\u03b9\u03ba\u03af\u03b1 15 \u03b5\u03c4\u03ce\u03bd \u03ac\u03c1\u03c7\u03b9\u03c3\u03b5 \u03bd\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03b5\u03b9 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc 2^127\u20131 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9 \u03b1\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2, \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03bc\u03b9\u03b1 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf \u03c0\u03bf\u03c5 \u03bf \u03af\u03b4\u03b9\u03bf\u03c2 \u03b5\u03af\u03c7\u03b5 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c8\u03b5\u03b9. \u03a4\u03bf 1876 \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc 19 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1 \u03b4\u03bf\u03ba\u03b9\u03bc\u03ce\u03bd \u03ba\u03b1\u03b9 \u03bc\u03ac\u03bb\u03b9\u03c3\u03c4\u03b1 \u03bc\u03b5 \u03c4\u03bf \u03c7\u03ad\u03c1\u03b9, \u03bf Lucas \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b5 \u03cc\u03c4\u03b9 \u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2^127\u20131 \u03c0\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 39 \u03c8\u03b7\u03c6\u03af\u03b1, \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2. \u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03af\u03b4\u03b9\u03b1 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf, \u03bf Lucas \u03b1\u03c0\u03ad\u03b4\u03b5\u03b9\u03be\u03b5 \u03c0\u03c9\u03c2 \u03bf Mersenne \u03b5\u03af\u03c7\u03b5 \u03c0\u03b1\u03c1\u03b1\u03bb\u03b5\u03af\u03c8\u03b5\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03ba\u03b1\u03c4\u03ac\u03bb\u03bf\u03b3\u03bf \u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd N \u03b3\u03b9\u03b1 \u03c4\u03bf\u03c5\u03c2 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5\u03c2 \u03bf 2^N\u20131 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2, \u03c4\u03bf\u03c5\u03c2 61, 89 \u03ba\u03b1\u03b9 107 \u03b5\u03bd\u03ce \u03b5\u03af\u03c7\u03b5 \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b9\u03bb\u03ac\u03b2\u03b5\u03b9 \u03bb\u03b1\u03bd\u03b8\u03b1\u03c3\u03bc\u03ad\u03bd\u03b1 \u03c4\u03bf 67.<\/p>\n
\u03a0\u03b1\u03c1\u03cc\u03bb\u03b7 \u03c4\u03b7 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ae \u03b4\u03bf\u03c5\u03bb\u03b5\u03b9\u03ac \u03c4\u03bf\u03c5 Lucas \u03c3\u03c4\u03bf\u03c5\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03c4\u03bf\u03c5 Mersenne, \u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2^257\u20131 \u03ae\u03c4\u03b1\u03bd \u03b1\u03ba\u03cc\u03bc\u03b1 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03cc\u03c1\u03b8\u03b7\u03c4\u03bf \u03ba\u03ac\u03c3\u03c4\u03c1\u03bf, \u03ce\u03c3\u03c0\u03bf\u03c5 \u03c4\u03bf 1930 \u03ad\u03bd\u03b1\u03c2 \u0391\u03bc\u03b5\u03c1\u03b9\u03ba\u03b1\u03bd\u03cc\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03bf Derrick Henry Lehmer \u03c3\u03b5 \u03b7\u03bb\u03b9\u03ba\u03af\u03b1 25 \u03b5\u03c4\u03ce\u03bd, \u03b2\u03b5\u03bb\u03c4\u03b9\u03ce\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf \u03c4\u03bf\u03c5 Lucas \u03bd\u03b1 \u03c1\u03af\u03be\u03b5\u03b9 \u03bb\u03af\u03b3\u03b7 \u03c3\u03ba\u03b9\u03ac \u03c3\u03c4\u03b7 \u03bb\u03b1\u03bc\u03c0\u03b5\u03c1\u03ae \u03c6\u03ae\u03bc\u03b7 \u03c4\u03bf\u03c5 Mersenne \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03cc\u03c4\u03b9 \u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2257\u20131 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 .
\n\u0397 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u03c4\u03bf\u03c5 Lehmer \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03bb\u03ae \u03c3\u03c4\u03b7\u03bd \u03c5\u03bb\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03b1\u03bb\u03bb\u03ac \u03ba\u03b1\u03c4\u03b1\u03c0\u03bb\u03b7\u03ba\u03c4\u03b9\u03ba\u03ae \u03c3\u03c4\u03b7 \u03c3\u03cd\u03bb\u03bb\u03b7\u03c8\u03ae \u03c4\u03b7\u03c2. \u039f Lehmer \u03b1\u03c0\u03ad\u03b4\u03b5\u03b9\u03be\u03b5 \u03cc\u03c4\u03b9 \u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 2^N\u20131 \u03bc\u03b5 \u039d \u03c0\u03c1\u03ce\u03c4\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc, \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03b1\u03bd \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03af \u03ad\u03bd\u03b1\u03bd \u03ac\u03bb\u03bb\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03c0\u03bf\u03c5 \u03bf\u03bd\u03bf\u03bc\u03ac\u03c3\u03c4\u03b7\u03ba\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 Lucas \u2013 Lehmer \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 L(N).
\n\u039f\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af Lucas \u2013 Lehmer \u03bf\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03b1\u03bd\u03b1\u03b4\u03c1\u03bf\u03bc\u03b9\u03ba\u03cc \u03c4\u03c1\u03cc\u03c0\u03bf. \u0388\u03c4\u03c3\u03b9 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03bf\u03bd L(N) \u03c5\u03c8\u03ce\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03bd \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03cc \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf \u03ba\u03b1\u03b9 \u03b1\u03c6\u03b1\u03b9\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03bf 2, \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae
\nL(N)=L(N\u20131)^2\u20132.
\n\u0393\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03b3\u03b9\u03b1 \u039d = 3 \u03b8\u03ad\u03c4\u03bf\u03c5\u03bc\u03b5 \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03b5\u03ba\u03ba\u03af\u03bd\u03b7\u03c3\u03b7\u03c2 L(3) = 14 \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bd\u03b5\u03c0\u03ce\u03c2:
\n$L(4) = 14^2 \u2013 2 = 194, L(5) = 194^2 \u2013 2 = 37634, L(6) = 37634^2 \u2013 2 = 1416317955$,\u2026
\n\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd 2^5\u20131=31 \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03af \u03c4\u03bf\u03bd L(5) = 37634 \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bd\u03b5\u03c0\u03ce\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2.<\/p>\n
\u039c\u03b5 \u03b1\u03c5\u03c4\u03cc \u03c4\u03bf\u03bd \u03c4\u03c1\u03cc\u03c0\u03bf \u03ba\u03bb\u03b5\u03af\u03bd\u03b5\u03b9 \u03bf \u03ba\u03cd\u03ba\u03bb\u03bf\u03c2 \u03c4\u03c9\u03bd \u03c0\u03c1\u03bf\u03b2\u03bb\u03ad\u03c8\u03b5\u03c9\u03bd \u03c4\u03bf\u03c5 Mersenne \u03ba\u03b1\u03b9 \u03b1\u03bd\u03bf\u03af\u03b3\u03b5\u03b9 \u03bf \u03b4\u03c1\u03cc\u03bc\u03bf\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b7 \u03ba\u03b1\u03b9 \u03ac\u03bb\u03bb\u03c9\u03bd \u03c0\u03c1\u03ce\u03c4\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd \u03c4\u03bf\u03c5 Mersenne \u03c0\u03bf\u03c5 \u03bb\u03cc\u03b3\u03c9 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c1\u03c6\u03ae\u03c2 \u03c4\u03bf\u03c5\u03c2 \u03c6\u03c4\u03ac\u03bd\u03bf\u03c5\u03bd \u03c3\u03b5 \u03b1\u03c0\u03af\u03c3\u03c4\u03b5\u03c5\u03c4\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03c8\u03b7\u03c6\u03af\u03c9\u03bd, \u03bc\u03cc\u03bd\u03bf \u03c0\u03bf\u03c5 \u03c4\u03ce\u03c1\u03b1 \u03bf\u03b9 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03af \u03b5\u03ba\u03c4\u03cc\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03b5\u03b8\u03cc\u03b4\u03bf\u03c5 Lucas \u2013 Lehmer ( Lucas \u2013 Lehmer primality test ) \u03ad\u03c7\u03bf\u03c5\u03bd \u03c3\u03c5\u03bc\u03bc\u03ac\u03c7\u03bf\u03c5\u03c2 \u03c4\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03bf\u03c5\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03ad\u03c2. \u039c\u03b5 \u03c4\u03b7\u03bd \u03b2\u03bf\u03ae\u03b8\u03b5\u03b9\u03ac \u03c4\u03bf\u03c5\u03c2 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03bf\u03af 48 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03c4\u03bf\u03c5 Mersenne \u03b5\u03ba \u03c4\u03c9\u03bd \u03bf\u03c0\u03bf\u03af\u03c9\u03bd \u03bf \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf 2^57885161\u20131 \u03c0\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 17.425.170 \u03c8\u03b7\u03c6\u03af\u03b1!!<\/p>\n
<\/p>\n
\u039f Martin Mersenne (\u039c\u03b5\u03c1\u03c3\u03ad\u03bd) (1588-1648) \u03ae\u03c4\u03b1\u03bd \u03ad\u03bd\u03b1\u03c2 \u0393\u03ac\u03bb\u03bb\u03bf\u03c2 \u03ba\u03b1\u03bb\u03cc\u03b3\u03b5\u03c1\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03c4\u03b1 \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd\u03c4\u03ac \u03c4\u03bf\u03c5 \u03b4\u03b5\u03bd \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03bd \u03bc\u03cc\u03bd\u03bf \u03c3\u03b5 \u03b8\u03c1\u03b7\u03c3\u03ba\u03b5\u03c5\u03c4\u03b9\u03ba\u03ac \u03b8\u03ad\u03bc\u03b1\u03c4\u03b1! \u0389\u03c4\u03b1\u03bd \u03b8\u03b5\u03bf\u03bb\u03cc\u03b3\u03bf\u03c2, \u03c6\u03b9\u03bb\u03cc\u03c3\u03bf\u03c6\u03bf\u03c2, \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03ba\u03b1\u03b9 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2. \u039b\u03ac\u03c4\u03c1\u03b5\u03c5\u03b5 \u03c4\u03b7 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 \u03ae\u03c4\u03b1\u03bd \u03bf \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03b1\u03bd\u03ad\u03c0\u03c4\u03c5\u03be\u03b5 \u03bc\u03b9\u03b1 \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03bc\u03ad\u03bd\u03b7 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03b1\u03c1\u03bc\u03bf\u03bd\u03af\u03b1\u03c2, \u03ad\u03c4\u03c3\u03b9 \u03c3\u03c5\u03c7\u03bd\u03ac \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03c9\u03c2…<\/p>\n","protected":false},"author":1,"featured_media":27902,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1,66],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?fit=900%2C609&ssl=1","rttpg_featured_image_url":{"full":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?fit=900%2C609&ssl=1",900,609,false],"landscape":["https:\/\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg",900,609,false],"portraits":["https:\/\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg",900,609,false],"thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=150%2C150&ssl=1",150,150,true],"medium":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?fit=300%2C203&ssl=1",300,203,true],"large":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?fit=900%2C609&ssl=1",900,609,true],"1536x1536":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?fit=900%2C609&ssl=1",900,609,true],"2048x2048":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?fit=900%2C609&ssl=1",900,609,true],"portfolio-square":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=570%2C570&ssl=1",570,570,true],"portfolio-portrait":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=600%2C609&ssl=1",600,609,true],"portfolio-landscape":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=800%2C600&ssl=1",800,600,true],"menu-featured-post":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=345%2C198&ssl=1",345,198,true],"qode-carousel_slider":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=400%2C260&ssl=1",400,260,true],"portfolio_slider":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=500%2C380&ssl=1",500,380,true],"portfolio_masonry_regular":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=500%2C500&ssl=1",500,500,true],"portfolio_masonry_wide":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=900%2C500&ssl=1",900,500,true],"portfolio_masonry_tall":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=500%2C609&ssl=1",500,609,true],"portfolio_masonry_large":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=900%2C609&ssl=1",900,609,true],"portfolio_masonry_with_space":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?fit=700%2C474&ssl=1",700,474,true],"latest_post_boxes":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=539%2C303&ssl=1",539,303,true],"woocommerce_thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=300%2C300&ssl=1",300,300,true],"woocommerce_single":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?fit=600%2C406&ssl=1",600,406,true],"woocommerce_gallery_thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2018\/08\/post-1429.jpg?resize=100%2C100&ssl=1",100,100,true]},"rttpg_author":{"display_name":"admin","author_link":"https:\/\/www.lecturesbureau.gr\/1\/author\/admin\/"},"rttpg_comment":0,"rttpg_category":"Uncategorized<\/a> \u0395\u03a0\u0399\u03a3\u03a4\u0397\u039c\u0397<\/a>","rttpg_excerpt":"\u039f Martin Mersenne (\u039c\u03b5\u03c1\u03c3\u03ad\u03bd) (1588-1648) \u03ae\u03c4\u03b1\u03bd \u03ad\u03bd\u03b1\u03c2 \u0393\u03ac\u03bb\u03bb\u03bf\u03c2 \u03ba\u03b1\u03bb\u03cc\u03b3\u03b5\u03c1\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03c4\u03b1 \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd\u03c4\u03ac \u03c4\u03bf\u03c5 \u03b4\u03b5\u03bd \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03bd \u03bc\u03cc\u03bd\u03bf \u03c3\u03b5 \u03b8\u03c1\u03b7\u03c3\u03ba\u03b5\u03c5\u03c4\u03b9\u03ba\u03ac \u03b8\u03ad\u03bc\u03b1\u03c4\u03b1! \u0389\u03c4\u03b1\u03bd \u03b8\u03b5\u03bf\u03bb\u03cc\u03b3\u03bf\u03c2, \u03c6\u03b9\u03bb\u03cc\u03c3\u03bf\u03c6\u03bf\u03c2, \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03ba\u03b1\u03b9 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2. \u039b\u03ac\u03c4\u03c1\u03b5\u03c5\u03b5 \u03c4\u03b7 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 \u03ae\u03c4\u03b1\u03bd \u03bf \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03b1\u03bd\u03ad\u03c0\u03c4\u03c5\u03be\u03b5 \u03bc\u03b9\u03b1 \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03bc\u03ad\u03bd\u03b7 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03b1\u03c1\u03bc\u03bf\u03bd\u03af\u03b1\u03c2, \u03ad\u03c4\u03c3\u03b9 \u03c3\u03c5\u03c7\u03bd\u03ac \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03c9\u03c2...","_links":{"self":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/27909"}],"collection":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/comments?post=27909"}],"version-history":[{"count":2,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/27909\/revisions"}],"predecessor-version":[{"id":27911,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/posts\/27909\/revisions\/27911"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/media\/27902"}],"wp:attachment":[{"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/media?parent=27909"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/categories?post=27909"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lecturesbureau.gr\/1\/wp-json\/wp\/v2\/tags?post=27909"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\u00a0http:\/\/www.mersenne.org\/<\/em><\/strong>
\n\u0395\u03b9\u03ba\u03cc\u03bd\u03b1 \u0391: https:\/\/gl.wikipedia.org\/wiki\/N%C3%BAmero_primo_de_Mersenne<\/em>
\n\u0395\u03b9\u03ba\u03cc\u03bd\u03b1 \u0392: https:\/\/www.amazon.in\/lorigine-recherche-scientifique-martin-mersenne\/dp\/2711752917<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"