Dan asked in Science & MathematicsMathematics · 1 decade ago

Consider the sequence of prime numbers 2, 3, 5, 7, 11, 13, 17, .... Let pi denote the ith number of the sequen

Consider the sequence of prime numbers 2, 3, 5, 7, 11, 13, 17, .... Let pi denote the ith number of the sequence, For example, p1=2, p2=3, p3=5, .... For i>0, Let

Pi = p1 × p2 × p3 × …×pi +1

Disprove the statement “Pi is a prime for all i>0.”.

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  • Anonymous
    1 decade ago
    Favorite Answer

    P6 = p1 × p2 × p3 × p4 × p5 × p6 + 1

    = 2 × 3 × 5 × 7 × 11 × 13 + 1

    = 30031 = 59 × 509

    P6 is not prime, and that disproves the statement.

  • 1 decade ago

    To disprove the statement, you must find a Pi which is not a prime. P6 = 2x3x5x7x11x13 + 1 is divisible by by 59. Check it out.

  • olli
    Lv 4
    4 years ago

    Any ordinary type is congruent to a million mod 2. for this reason 5 ordinary numbers would be congruent to 5 mod 2, that's congruent to a million. yet 50 is congruent to 0 mod 2, which ability there is no answer.

  • 1 decade ago

    p8=19 p9=23 p10=29

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