World!OfNumbers |
WON plate 188 | |
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[ How many different primes divide all the pandigitals ? (each digit from set [1-9] or [0-9] appears just once)
What is the largest prime factor in each case ?
What prime factor(s) has the least frequency of appearing ?
How many palindromic prime factors are there in both cases ?
List of smallest and largest nine-/pandigital 3
Some related sources
A178775 Smallest prime factors of zerofull restricted pandigital numbers.
A216203 Smallest prime that does not divide at least one n-digit zeroless pandigital number.
Puzzle 259 Not dividing any pandigital. |

Questions | Answers by Alexandru Petrescu [ April 4, 2021 ] | |
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Ninedigitals | Pandigitals | |

How many different primes divide all the nine- and pandigitals ? | 36419 | 252702 |

What is the largest prime factor ? | 109739359 * 9 = 987654231 | 1097393447 * 9 = 9876541023 |

How many palindromic prime factors appear ? | 23 | 104 |

Can you list them ? | 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 1093901, 9561659, 9583859 | |

The largest palindromic prime factor ? | 9583859 * 27 = 258764193 | 955141559 * 9 = 8596274031 |

Prime factors having the least frequency of appearing ? | There are many 9digits prime factors, when multiplied by 9 provide a unique ninedigital ! | There are many 10digits prime factors, when multiplied by 10 provide a unique pandigital ! |

Numbers = 3^{k} * p * q ;(3, p, q distinct primes) | Semiprimes topic total numbers [version A] | |

75330 | 565732 | |

Smallest | ||

123456789 = 3^{2} * 3607 * 3803 | 1023456789 = 3^{4} * 2221 * 5689 | |

Largest | ||

987654123 = 3^{2} * 109 * 1006783 | 9876542103 = 3^{2} * 53 * 20705539 | |

Numbers = 3^{k} * p ;(3, p distinct primes) | Semiprimes topic total numbers [version B] | |

35319 | 249804 | |

Smallest | ||

123458679 = 3^{2} * 13717631 | 1023456879 = 3^{2} * 113717431 | |

Largest | ||

987654231 = 3^{2} * 109739359 | 9876542301 = 3^{8} * 1505341 |

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A000188 Prime Curios! Prime Puzzle Wikipedia 188 Le nombre 188 |

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