This could cause changes in cryptography which would then flow on to the rest of everything. 0000072044 00000 n 0000048635 00000 n 0000077144 00000 n 1656 73 So the twin prime conjecture is not that important of a result itself, but it is a hard enough problem that if someone were to solve it, it would probably require discovering some new mathematics related to how we think about prime numbers, which would open up the possibilities of other types of questions we could answer.

So the twin prime conjecture is not that important of a result itself, but it is a hard enough problem that if someone were to solve it, it would probably require discovering some new mathematics related to how we think about prime numbers, which would open up the possibilities of other types of questions we could answer. 0000005433 00000 n We talk to three of this year's winners of the prestigious Whitehead Prizes. There are two related conjectures, each called the twin prime conjecture. If it is ever solved, what other problems in mathematics would be affected?

*��4Z�{�-���#�wxf:-Z�Pi��9Y��_,=�۵���|����:��/O�M����U}ё����?,s�������p2��������z[�8u�,�����JH�J��{�����Xske^�@�)Q�I>�n�DL7.-d�~v�,�s�6%�oy�z|�_l��C�ɒ��Wx,O��z|u����k�Z�2����0���)Z�`kϯ�y#~Vڢ�c���ӳt�J�O�|+�$`�V.����4��ř��>^n;1�(��ɡ��Zh���)Z�m� �U��r����fs�����~�9�>���}�d��������$�>=�3����>!�bpqs����L������ ߮ �\6lQ'(�}����Y�v�!���0�F�)F���{��{< f�1��-ȝj+�LJ �W��[m �Pp~a�^(RW�}������~�9���Lx����l-H�Jp� S��Y����{�wS����� 0000081766 00000 n The first version states that there are an infinite number of pairs of twin primes (Guy 1994, p. 19).

0000036401 00000 n This year has seen a flurry of results as mathematicians hunt down the elusive proof of the twin prime conjecture. Will they get their wish for Christmas this year? 0000010107 00000 n (interval). 0000005262 00000 n 0000002925 00000 n

0000038960 00000 n 0000093614 00000 n 0000078219 00000 n Primes are important for cryptography. 0000093289 00000 n 0000062364 00000 n 0000017949 00000 n 0000000016 00000 n There's been progress on one of the biggest open problems in maths: the twin prime conjecture. 0000007068 00000 n x�b```b`�f`g``}� Ȁ �@1v�6���Aº���X���ʡ|A��}���< �'00x�~Yѿ�+U��B���Tu�Fu��!�����L5*�93=�TVL�u�ߚ��ŉ��b��\��w�V�ͮ�s xref 0000077345 00000 n �+D�@�����v�r��?�3��?\�?�?X�Pϲ��Aj�� #��5���,�!R,�v54020�e����a�t/�,�3�;�/(+W9Lf������=�h��� k>��`;( ���(�p]dS��N+�6�N�}LL;���2X1. 0000063438 00000 n 0 Yitang Zhang proved that there are an infinite number of pairs of primes that differ by n, where n is some number less than 70 million or so. But...proving there are infinitely many twin primes doesn’t mean there are patterns to where they show up? 0000019137 00000 n 0000003933 00000 n 0000091358 00000 n

The Twin Prime Conjecture. 1728 0 obj<>stream

0000093483 00000 n Copyright © 1997 - 2020. 0000090665 00000 n If they differ by anything else, they are not twin primes. University of Cambridge. $\begingroup$ You didn't even mention twin prime conjecture.