מספר מזל (מתמטיקה)

אנימציה המתארת את ניפוי מספרי המזל. המספרים באדום הם מספרי המזל.

במתמטיקה, מספר מזל הוא מספר השייך לתת קבוצה של המספרים הטבעיים, המכילה מספרים שנותרו לאחר ניפוי בשיטה דומה לשיטת הנפה של ארטוסתנס המוצאת ראשוניים.

אלגוריתם הניפוי למציאת מספרי מזל:

נתחיל בסדרת המספרים הטבעיים החל מ־1:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, ...

ואז ננפה את כל המספרים הזוגיים:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, ...

המספר השני בסדרה הוא 3, ולכן ננפה כעת כל מספר שלישי בסדרה:

1, 3, 7, 9, 13, 15, 19, 21, ...

המספר השלישי בסדרה הוא 7, ולכן ננפה כעת כל מספר שביעי בסדרה:

1, 3, 7, 9, 13, 15, 21, ...

וכן הלאה.

המספרים הנותרים בסוף התהליך נקראים "מספרי מזל"; מספרם אינסופי. המספרים הראשונים בסדרה זו הם:

1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99 ...

לקבוצת מספרי המזל יש כמה תכונות דומות לאלו של המספרים הראשוניים; למשל, שכיחותם האסימפטוטית דומה לזו שקובע משפט המספרים הראשוניים (כלומר, יש בערך מספרי מזל בין 1 ל- x). לא ידוע האם יש אינסוף מספרי מזל שהם בעת ובעונה אחת מספרים ראשוניים.

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