

A307890


Prime centuries with at least one prime year in each decade and exactly one prime year in decades 1 to 8.


1



3677, 4073, 16447, 118463, 211217, 357131, 368153, 582017, 932413, 1172777, 1239443, 2284027, 2421473, 3900931, 4943777, 5046053, 6850463, 6966059, 8046347, 10448783, 11548777, 12849937, 15198811, 16031237, 17315087, 19443679, 20075687, 20434811, 20462861, 20614667
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OFFSET

1,1


COMMENTS

In other words, prime numbers p such that there are ten consecutive primes between p*100100 and p*100, each of them in a different decade. (The Pdiv10s are all different.)  Don Reble, May 02 2019


LINKS



EXAMPLE

4073 is in the sequence, representing the prime sequence 407203, 407207, 407219, 407221, 407233, 407249, 407257, 407263, 407273, 407287, 407291, 407299, with 2 primes in decades 0 and 9, and 1 prime in decades 1 to 8.  R. J. Mathar, May 03 2019


MAPLE

isA307890 := proc(n)
local p, dec ;
if not isprime(n) then
false;
else
p := 100*(n1) ;
p := prevprime(p+10) ;
for dec from 0 to 9 do
if modp(floor(p/10), 10) <> dec then
return false;
end if;
p := nextprime(p) ;
end do:
true ;
end if;
end proc:
for i from 1 do
p := ithprime(i) ;
if isA307890(p) then
printf("%d, \n", p) ;
end if;


CROSSREFS



KEYWORD

nonn,less


AUTHOR



STATUS

approved



