A376907
a(n) is the least n-digit cuban prime.
Original entry on oeis.org
7, 19, 127, 1657, 10267, 102121, 1021417, 10052191, 100381321, 1000556719, 10000510297, 100025541019, 1000011191887, 10000028937841, 100000062634561, 1000001305386991, 10000001240507791, 100000021541868691, 1000000084213608427, 10000000012591553221, 100000000159478313337
Offset: 1
-
nextcuban:= proc(n)
local k,y;
for k from ceil((sqrt(12*n-3)-3)/6) do
y:= (k+1)^3 - k^3;
if isprime(y) then return y fi
od
end proc:
seq(nextcuban(10^i), i = 0 .. 25); # Robert Israel, Nov 08 2024
-
a[n_]:=Module[{k=1},While[!PrimeQ[m=3k^2+3k+1]||IntegerLength[m]
-
from itertools import count
from math import isqrt
from sympy import isprime
def A376907(n):
for k in count(isqrt((((a:=10**(n-1))<<2)-1)//12)):
m = 3*k*(k+1)+1
if m >= a and isprime(m):
return m # Chai Wah Wu, Oct 13 2024
A099667
a(n) is the largest prime before A002281(n); repdigits repeating 7.
Original entry on oeis.org
5, 73, 773, 7759, 77773, 777769, 7777769, 77777761, 777777773, 7777777741, 77777777767, 777777777773, 7777777777771, 77777777777753, 777777777777773, 7777777777777753, 77777777777777747, 777777777777777743
Offset: 1
-
Table[NextPrime[7 (10^n - 1)/9, -1], {n, 35}]
(* Second program: *)
Rest[NextPrime[#,-1]&/@LinearRecurrence[{11,-10},{0,7},25]] (* Harvey P. Dale, May 24 2015 *)
A115062
Prime nearest to 10^n. In case of a tie, choose the smaller.
Original entry on oeis.org
2, 11, 101, 997, 10007, 100003, 1000003, 9999991, 100000007, 1000000007, 10000000019, 100000000003, 999999999989, 9999999999971, 99999999999973, 999999999999989, 10000000000000061, 99999999999999997, 1000000000000000003, 9999999999999999961
Offset: 0
-
a:= n-> (t->((p, q)->`if`(q-tAlois P. Heinz, Aug 13 2014
-
Table[Min[Nearest[{NextPrime[10^n],NextPrime[10^n,-1]},10^n]],{n,0,20}] (* Harvey P. Dale, Mar 14 2023 *)
-
for(n=0, 20, a=10^n-precprime(10^n); b=nextprime(10^n)-10^n; if(a<=b && n!=0, print1(precprime(10^n), ", "), print1(nextprime(10^n), ", "))) \\ Felix Fröhlich, Aug 13 2014
A139052
Array read by rows: row n lists the first two primes with n digits.
Original entry on oeis.org
2, 3, 11, 13, 101, 103, 1009, 1013, 10007, 10009, 100003, 100019, 1000003, 1000033, 10000019, 10000079, 100000007, 100000037, 1000000007, 1000000009, 10000000019, 10000000033, 100000000003, 100000000019, 1000000000039, 1000000000061
Offset: 1
-
ftp[d_]:=Module[{np1=NextPrime[10^(d-1)]},{np1,NextPrime[np1]}]; Array[ ftp,15]//Flatten (* Harvey P. Dale, Mar 27 2021 *)
A139535
Smallest prime starting with 1 that contains exactly n 0's.
Original entry on oeis.org
101, 1009, 10007, 100003, 1000003, 100000037, 100000007, 1000000007, 100000000019, 100000000003, 10000000000037, 100000000000031, 1000000000000037, 10000000000000061, 100000000000000013
Offset: 1
-
sp0[n_]:=Module[{c=1,d},While[d=FromDigits[Join[PadRight[{1},n+1,0],IntegerDigits[ c]]];DigitCount[d,10,0]>n||CompositeQ[d],c=c+2];FromDigits[ Join[ PadRight[ {1},n+1,0],IntegerDigits[c]]]]; Array[sp0,20] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 30 2020 *)
A157033
Smallest prime with 2^n digits.
Original entry on oeis.org
2, 11, 1009, 10000019, 1000000000000037, 10000000000000000000000000000033, 1000000000000000000000000000000000000000000000000000000000000121
Offset: 0
-
f[n_] := NextPrime[10^(2^n - 1)]; Table[f@n, {n, 0, 7}] (* Robert G. Wilson v, Mar 17 2009 *)
A340487
a(n) is the least prime that is the concatenation of two n-digit primes, or 0 if there are none.
Original entry on oeis.org
23, 1117, 101107, 10091021, 1000710181, 100003100129, 10000031000171, 1000001910000349, 100000007100000541, 10000000071000000349, 1000000001910000000319, 100000000003100000000063, 10000000000391000000000903, 1000000000003710000000000259, 100000000000031100000000000403
Offset: 1
a(3) = 101107 is prime and the concatenation of the two 3-digit primes 101 and 107.
-
f:= proc(d) local P,a,b;
a:= prevprime(10^(d-1));
do
a:= nextprime(a);
if a > 10^d then return FAIL fi;
b:= prevprime(10^(d-1));
do
b:= nextprime(b);
if b > 10^d then break fi;
if isprime(10^d*a+b) then return 10^d*a+b fi;
od od:
FAIL
end proc:
f(1):= 23:
map(f, [$1..20]);
A382899
The smallest n-digit prime that turns composite at each step as its digits are successively appended, starting from the first.
Original entry on oeis.org
2, 11, 101, 1013, 10007, 100003, 1000003, 10000019, 100000007, 1000000007, 10000000019, 100000000003, 1000000000061, 10000000000037, 100000000000031, 1000000000000037, 10000000000000061, 100000000000000013, 1000000000000000003, 10000000000000000051
Offset: 1
a(1) = 2, because 2 is prime, 22 = 2*11 is composite, while no smaller one-digit prime exhibits this property.
a(2) = 11, because 11 is prime, 111 = 3*37 and 1111 = 11*101 are composite, while no smaller two-digit prime exhibits this property.
a(4) = 1013, because 1013 is prime, 10131 = 3 * 11 * 30, 101310 = 2 * 3 * 5 * 11 * 307, 1013101 = 227 * 4463 and 10131013 = 73 * 137 * 1013 are composite, while no smaller 4-digit prime exhibits this property.
-
isok(p, n) = my(d=digits(p)); for (i=1, #d, p = 10*p+d[i]; if (isprime(p), return(0));); return(1);
a(n) = my(p=nextprime(10^(n-1))); while (!isok(p, n), p = nextprime(p+1)); p; \\ Michel Marcus, Apr 09 2025
-
from sympy import isprime, nextprime
def c(s): # check if prime p's string of digits meets the concatenation condition
return not any(isprime(int(s:=s+c)) for c in s)
def a(n):
p = nextprime(10**(n-1))
while not c(str(p)): p = nextprime(p)
return p
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Apr 09 2025
A382981
The smallest n-digit prime that turns composite at each step as its digits are successively appended, starting from the last.
Original entry on oeis.org
2, 11, 101, 1019, 10007, 100043, 1000003, 10000019, 100000007, 1000000007, 10000000019, 100000000003, 1000000000039, 10000000000037, 100000000000031, 1000000000000037, 10000000000000061, 100000000000000003, 1000000000000000003, 10000000000000000051
Offset: 1
a(4) = 1019, because 1019 is prime and 10199 = 7 * 31 * 47, 101991 = 3 * 33997, 1019910 = 2 * 3 * 5 * 33997 and 10199101 = 11 * 927191 are composite, while no smaller 4-digit prime exhibits this property.
-
ok[p_] := Block[{d = IntegerDigits@p}, d = Join[d, Reverse@ d]; And @@ CompositeQ /@ (FromDigits[d[[;; #]]] & /@ Range[Length[d]/2 + 1, Length@d])]; a[n_] := Block[{p = NextPrime[10^(n-1)]}, While[! ok[p], p = NextPrime@p]; p]; Array[a, 20] (* Giovanni Resta, Apr 11 2025 *)
-
from sympy import isprime, nextprime
def c(s): # check if prime p's string of digits meets the concatenation condition
return not any(isprime(int(s:=s+c)) for c in s[::-1])
def a(n):
p = nextprime(10**(n-1))
while not c(str(p)): p = nextprime(p)
return p
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Apr 16 2025
A073862
Difference between the largest and the smallest n-digit prime.
Original entry on oeis.org
5, 86, 896, 8964, 89984, 899980, 8999988, 89999970, 899999930, 8999999960, 89999999958, 899999999986, 8999999999932, 89999999999936, 899999999999958, 8999999999999900, 89999999999999936, 899999999999999986, 8999999999999999958, 89999999999999999938
Offset: 1
a(3) = 997 - 101 = 896.
a(1) = 5 because 7-2 = 5.
-
seq(prevprime(10^n)-nextprime(10^(n-1)), n=1..21); # Emeric Deutsch, Mar 28 2005
-
Table[NextPrime[10^(n+1),-1]-NextPrime[10^n],{n,0,18}] (* Harvey P. Dale, May 04 2016 *)
Comments