The Goldbach conjecture -the Goldbach glacier- for the even numbers from 6 to 1564 [La conjecture de Goldbach -le glacier de Goldbach- pour les entiers pairs de 6 à 1564].




The Goldbach conjecture states that each even integer number N greater or equal to 4 can be written as the sum of two prime numbers. For example:
                    4   = 2+2
                    6   = 3+3
                    8   = 3+5 [= 5+3]
                    10  = 3+7 = 5+5 [= 7+3]
                    (...)
                    70  = 3+67 = 11+59 = 17+53 = 23+47 = 29+41 [= 41+29 = 47+23 = 53+17 = 59+11 = 67+3]
                    (...)
                    990 = 7+983 = 13+977 = 19+971 = 23+967 = 37+953 = 43+947 = 53+937 = 61+929 = 71+919 = 79+911 = 83+907 = 103+887 = 107+883 = 109+881 = 113+877 = 127+863 = 131+859 = 137+853 = 151+839 = 163+827 = 167+823 = 179+811 = 181+809 = 193+797 = 229+761 = 233+757 = 239+751 = 251+739 = 257+733 = 263+727 = 271+719 = 281+709 = 307+683 = 313+677 = 317+673 = 331+659 = 337+653 = 347+643 = 349+641 = 359+631 = 373+617 = 383+607 = 389+601 = 397+593 = 419+571 = 421+569 = 433+557 = 443+547 = 449+541 = 467+523 = 487+503 = 491+499 [= 499+491 = 503+487 = 523+467 = 541+449 = 547+443 = 557+433 = 569+421 = 571+419 = 593+397 = 601+389 = 607+383 = 617+373 = 631+359 = 641+349 = 643+347 = 653+337 = 659+331 = 673+317 = 677+313 = 683+307 = 709+281 = 719+271 = 727+263 = 733+257 = 739+251 = 751+239 = 757+233 = 761+229 = 797+193 = 809+181 = 811+179 = 823+167 = 827+163 = 839+151 = 853+137 = 859+131 = 863+127 = 877+113 = 881+109 = 883+107 = 887+103 = 907+83 = 911+79 = 919+71 = 929+61 = 937+53 = 947+43 = 953+37 = 967+23 = 971+19 = 977+13 = 983+7]
                    (...)


The vertical axis represents the rank R={0, 1, 2, 3,...} of the prime number starting at 3 (excluding the first one -2-). For example:
                    rank(3) = 0
                    rank(5) = 1
                    rank(7) = 2
                    (...)
                    rank(P) = R
                    (...)
(each rank is displayed as a single point).

When the horizontal axis represents the even numbers N={6, 8, 10, 12,...} starting at 6 (this process does not start at 4=2+2 in order to avoid the first prime number -2 that is an even number- on the vertical axis). Each N-vertical line exhibits the decompositions of N as sums of two prime numbers (N=PrimeNumber(R1)+PrimeNumber(R2), R1 and R2 having the same color).


See some related visualizations (including this one):

 
 
 
 



(CMAP28 WWW site: this page was created on 01/11/2013 and last updated on 10/20/2016 11:17:09 -CEST-)



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