Assuming a lifespan of 80 years, in what years of the 20th and 21st centuries (1900-1999), (2000-2099) would you have to be born to have the maximum number of prime birthdays in a prime year?

In what years of the same time spans would you have to be born to have the minimum number of prime birthdays in a prime year?

You may assume that people born on Feb. 29 in a leap year still celebrate their birthdays each following year.

The birth years with their number of doubly prime years are:

1900  5 1901  0 1902  6 1903  0 1904  3 1905  1 1906  4 1907  0 1908  6 1909  0
1910  3 1911  1 1912  4 1913  0 1914  6 1915  0 1916  2 1917  0 1918  4 1919  0
1920  9 1921  0 1922  3 1923  0 1924  3 1925  0 1926  9 1927  0 1928  5 1929  1
1930  5 1931  1 1932  8 1933  0 1934  3 1935  0 1936  5 1937  0 1938  7 1939  0
1940  5 1941  0 1942  4 1943  0 1944  8 1945  0 1946  6 1947  1 1948  3 1949  1
1950  9 1951  0 1952  3 1953  0 1954  3 1955  0 1956 10 1957  0 1958  5 1959  0
1960  6 1961  0 1962  6 1963  0 1964  4 1965  0 1966  6 1967  0 1968  9 1969  0
1970  7 1971  1 1972  3 1973  0 1974  9 1975  0 1976  6 1977  1 1978  2 1979  0
1980 10 1981  0 1982  6 1983  0 1984  5 1985  1 1986  9 1987  0 1988  5 1989  0
1990  6 1991  1 1992  8 1993  0 1994  5 1995  1 1996  6 1997  1 1998  7 1999  0
2000  5 2001  1 2002  4 2003  0 2004  5 2005  0 2006  4 2007  0 2008  6 2009  1
2010 10 2011  0 2012  4 2013  0 2014  4 2015  1 2016  9 2017  0 2018  2 2019  0
2020  6 2021  0 2022  9 2023  0 2024  4 2025  1 2026  6 2027  1 2028  6 2029  0
2030  3 2031  0 2032  5 2033  0 2034  6 2035  0 2036  4 2037  1 2038  4 2039  0
2040  9 2041  0 2042  4 2043  0 2044  4 2045  0 2046  8 2047  0 2048  2 2049  0
2050  7 2051  1 2052  9 2053  0 2054  2 2055  0 2056  5 2057  0 2058 10 2059  0
2060  5 2061  1 2062  5 2063  0 2064  8 2065  0 2066  5 2067  1 2068  6 2069  0
2070 12 2071  0 2072  5 2073  0 2074  5 2075  0 2076  9 2077  0 2078  5 2079  1
2080  6 2081  1 2082 10 2083  0 2084  6 2085  1 2086  4 2087  1 2088  6 2089  0
2090  5 2091  0 2092  4 2093  0 2094  8 2095  0 2096  4 2097  1 2098  3 2099  0
2100 10

The year 2100 has been included so that any definition of the 21st century can be counted.

The largest number is 12, for someone born in 2070

The program to produce this is

 5   cls
10   for Y=1900 to 2100
20    T=0
30    for Age=1 to 80
40      if nxtprm(Y+Age-1)=Y+Age and nxtprm(Age-1)=Age then T=T+1
50    next Age
60    Row=(Y-1900)\10:Col=((Y-1900)@10)*8
70    locate Col,Row:print using(5,0),Y;using(3,0),T;
80   next Y

A different program details the years and ages of a person to be born in 2070:

2070
2081    11
2083    13
2087    17
2089    19
2099    29
2111    41
2113    43
2129    59
2131    61
2137    67
2141    71
2143    73

The minimum is zero, as anyone born in an odd year that's not two years before a prime year will always have his prime ages in even years, except for the second birthday, which in the cases considered is not prime.

Posted by Charlie on 2005-03-23 20:35:17