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Sierpiński number of the first kind

A Sierpiński number of the first kind is a number of the form . The first few are 2, 5, 28, 257, 3126, 46657, 823544, 16777217, ... (OEIS A014566). Sierpiński proved that if is prime with , then must be of the form , making a Fermat number with . The first few of this form are 1, 3, 6, 11, 20, 37, 70, ... (OEIS A006127).The numbers of digits in the number is given bywhere is the ceiling function, so the numbers of digits in the first few candidates are 1, 3, 20, 617, 315653, 41373247568, ... (OEIS A089943).The only known prime Sierpiński numbers of the first kind are 2, 5, 257, with the first unknown case being . The status of Sierpiński numbers is summarized in the table below (Nielsen).status of 01prime ()13prime ()26composite with factor 311composite with factor 420composite with no factor known537composite with factor 670unknown7135unknown8264unknown9521unknown101034unknown112059composite with factor 124108unknown138205unknown1416398unknown1532783unknown1665552unknown17131089unknown..

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