A074668 -id:A074668 - cp's OEIS frontend

A074667 Seven-digit distinct-digit primes.

1023467, 1023487, 1023697, 1023769, 1023857, 1023947, 1024357, 1024379, 1024579, 1024589, 1024693, 1024697, 1024783, 1024853, 1024957, 1024963, 1024987, 1025347, 1025483, 1025693, 1025749, 1025789, 1025839, 1025873, 1025897, 1026359, 1026439

Offset: 1

Zak Seidov, Aug 30 2002

The last term is a(33950) = 9876413. - Giovanni Resta, Mar 19 2013

There are 33,950 terms in the sequence. - Harvey P. Dale, Jun 01 2024

			a(1)=1023467 because it is the first (smallest) 7-digit prime with all distinct digits.

Daniel Starodubtsev, Table of n, a(n) for n = 1..33950 (complete sequence, terms 1..10000 from Nathaniel Johnston)

The first differences are in A074668.

Cf. A073532 (Number of n-digit primes with all digits distinct). - Jon E. Schoenfield, Aug 13 2017

lim:=pi(1026439): for n from pi(1000000) to lim do p:=ithprime(n): d:=[op(convert(p, base, 10))]: ddig:=true: for k from 0 to 9 do if(numboccur(k, d)>1)then ddig:=false: break: fi: od: if(ddig)then printf("%d, ", p): fi: od: # Nathaniel Johnston, Jun 22 2011

Select[Range[1023457, 9876543, 2], Length[Union[IntegerDigits[ # ]]]==7 &&PrimeQ[ # ]&]
Select[FromDigits/@Permutations[Range[0,9],{7}],IntegerLength[#]==7&&PrimeQ[#]&] (* Harvey P. Dale, Jun 01 2024 *)

is(n)=isprime(n) && #digits(n)==7 && #Set(digits(n))==7 \\ Charles R Greathouse IV, Feb 11 2017

A074671 Five-digit distinct-digit primes.

Original entry on oeis.org

10243, 10247, 10253, 10259, 10267, 10273, 10289, 10357, 10369, 10427, 10429, 10453, 10457, 10459, 10463, 10487, 10529, 10567, 10589, 10597, 10627, 10639, 10657, 10687, 10723, 10729, 10739, 10753, 10789, 10837, 10847, 10853, 10859, 10867, 10937, 10957

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 2529 five-digit primes with all distinct digits. The end of the sequence is: 97241, 97283, 97301, 97381, 97423, 97453, 97463, 97501, 97523, 97561, 97583, 97613, 97651, 97813, 97841, 97843, 97861, 98017, 98041, 98047, 98057, 98123, 98143, 98207, 98213, 98251, 98257, 98317, 98321, 98327, 98347, 98407, 98453, 98467, 98473, 98507, 98543, 98561, 98563, 98573, 98621, 98627, 98641, 98713, 98731.

			a(1)=10243 and a(2529)=98731 because these are the first and the last 5-digit primes with all distinct digits.

Nathaniel Johnston, Table of n, a(n) for n = 1..2529 (full sequence)

The first differences are in A074672. 4-digit distinct-digit primes are in A074673. 6-digit distinct-digit primes are in A074669, see also A074670. 7-digit distinct-digit primes are in A074667, see also A074668. 8-digit distinct-digit primes are in A074665, see also A074666.

Select[Range[10243, 98731, 2], Length[Union[IntegerDigits[ # ]]]==5&&PrimeQ[ # ]&]
Select[Prime[Range[1230,9592]],Max[DigitCount[#]]==1&] (* Harvey P. Dale, Mar 16 2016 *)

is(n)=isprime(n) && #digits(n)==5 && #Set(digits(n))==5 \\ Charles R Greathouse IV, Feb 11 2017

A074673 Four-digit distinct-digit primes.

Original entry on oeis.org

1039, 1049, 1063, 1069, 1087, 1093, 1097, 1237, 1249, 1259, 1279, 1283, 1289, 1297, 1307, 1327, 1367, 1409, 1423, 1427, 1429, 1439, 1453, 1459, 1483, 1487, 1489, 1493, 1523, 1543, 1549, 1567, 1579, 1583, 1597, 1607, 1609, 1627, 1637, 1657, 1693, 1697

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 510 four-digit primes with all distinct digits. The end of the sequence is: 8761, 8923, 8941, 8951, 8963, 8971, 9013, 9041, 9043, 9067, 9103, 9127, 9137, 9157, 9173, 9187, 9203, 9241, 9257, 9281, 9283, 9341, 9371, 9403, 9413, 9421, 9431, 9437, 9461, 9463, 9467, 9473, 9521, 9547, 9587, 9601, 9613, 9623, 9631, 9643, 9721, 9743, 9781, 9803, 9817, 9851, 9857, 9871.

			a(1) = 1039 and a(510) = 9871 because these are the first and the last four-digit primes with all distinct digits.

Nathaniel Johnston, Table of n, a(n) for n = 1..510 (full sequence)

The first differences are in A074674. 5-digit distinct-digit primes are in A074671, see also A074672. 6-digit distinct-digit primes are in A074669, see also A074670. 7-digit distinct-digit primes are in A074667, see also A074668. 8-digit distinct-digit primes are in A074665, see also A074666.

Select[Range[1001, 9999, 2], Length[Union[IntegerDigits[#]]] == 4 && PrimeQ[#] &] (* Corrected by Harvey P. Dale, Jan 17 2011 *)
Select[Prime[Range[168,1229]],Max[DigitCount[#]]==1&] (* Harvey P. Dale, Aug 22 2019 *)

is(n)=isprime(n) && #digits(n)==4 && #Set(digits(n))==4 \\ Charles R Greathouse IV, Feb 11 2017

A074669 Six-digit distinct-digit primes.

Original entry on oeis.org

102359, 102367, 102397, 102437, 102497, 102539, 102547, 102563, 102587, 102593, 102643, 102647, 102653, 102673, 102679, 102763, 102769, 102793, 102859, 102953, 102967, 102983, 103289, 103457, 103529, 103549, 103567, 103657, 103687, 103769, 103867, 103967, 104239

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 10239 six-digit primes with distinct digits.

			a(1)=102359 because it is the first (smallest) 6-digit primes with all distinct digits.

Nathaniel Johnston, Table of n, a(n) for n = 1..10239 (full sequence)

The first differences are in A074670. 7-digit distinct-digit primes are in A074667, see also A074668. 8-digit distinct-digit primes are in A074665, see also A074666.

Select[Range[100001, 999999, 2], Length[Union[IntegerDigits[ # ]]]==6 && PrimeQ[ # ]&]
Take[Select[Prime[Range[PrimePi[100000]+1,PrimePi[999999]]],Max[DigitCount[#]]==1&],50] (* Harvey P. Dale, Jan 09 2011 *)
Select[Sort[FromDigits/@Flatten[Permutations/@Subsets[Range[0,9],{6}],1]], IntegerLength[#] == 6&&PrimeQ[#]&] (* Harvey P. Dale, Jul 28 2017 *)

is(n)=isprime(n) && #digits(n)==6 && #Set(digits(n))==6 \\ Charles R Greathouse IV, Feb 11 2017

A074670 Differences between successive six-digit distinct-digit primes.

Original entry on oeis.org

8, 30, 40, 60, 42, 8, 16, 24, 6, 50, 4, 6, 20, 6, 84, 6, 24, 66, 94, 14, 16, 306, 168, 72, 20, 18, 90, 30, 82, 98, 100, 272, 48, 10, 30, 42, 158, 10, 42, 14, 4, 26, 16, 20, 24, 10, 30, 6, 30, 30, 38, 42, 10, 74, 34

Offset: 1

Zak Seidov, Aug 30 2002

There are 10238 terms in this sequence, all of which are in the b-file. - Harvey P. Dale, Jun 06 2018

			a(1)=8 & a(2)=30 because first three 6-digit distinct-digit primes are 102359, 102367, 102397 and differences between them are 8 and 30.

Harvey P. Dale, Table of n, a(n) for n = 1..10238

The first differences of A074669. For 3-digit distinct-digit primes, see A074675, A074676. For 4-digit distinct-digit primes, see A074673, A074674. For 5-digit distinct-digit primes, see A074671, A074672. For 7-digit distinct-digit primes, see A074667, A074668. For 8-digit distinct-digit primes, see A074665, A074666.

a=102345; b=a+8000; se6 = Select[Range[a, b, 2], Length[Union[IntegerDigits[ # ]]] == 6 && PrimeQ[ # ] & ]; Flatten[Table[{se6[[i+1]]-se6[[i]]}, {i, Length[se6]-1}]]
Select[Prime[Range[9593,78498]],Length[Union[IntegerDigits[#]]] == 6&] // Differences (* Harvey P. Dale, Jun 06 2018 *)

A074675 Three-digit distinct-digit primes.

Original entry on oeis.org

103, 107, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 317, 347, 349, 359, 367, 379, 389, 397, 401, 409, 419, 421, 431, 439, 457, 461, 463, 467, 479, 487, 491, 503, 509, 521, 523, 541

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 97 three-digit primes with all distinct digits, so the sequence is finite.

			a(1)=103 and a(97)=983 because these are the first and the last three-digit primes with all distinct digits.

Nathaniel Johnston, Table of n, a(n) for n = 1..97 (full sequence)

The first differences are in A074676. 4-digit distinct-digit primes are in A074673, see also A074674. 5-digit distinct-digit primes are in A074671, see also A074672. 6-digit distinct-digit primes are in A074669, see also A074670. 7-digit distinct-digit primes are in A074667, see also A074668. 8-digit distinct-digit primes are in A074665, see also A074666.

Select[Range[103, 983, 2], Length[Union[IntegerDigits[ # ]]]==3&&PrimeQ[ # ]&]
Select[Prime[Range[26,168]],Length[Union[IntegerDigits[#]]]==3&] (* Harvey P. Dale, Jan 14 2020 *)

A074672 Differences between successive five-digit distinct-digit primes.

Original entry on oeis.org

4, 6, 6, 8, 6, 16, 68, 12, 58, 2, 24, 4, 2, 4, 24, 42, 38, 22, 8, 30, 12, 18, 30, 36, 6, 10, 14, 36, 48, 10, 6, 6, 8, 70, 20, 16, 14, 1050, 6, 6, 24, 24, 250, 32, 30, 28, 20, 16, 6, 8, 10, 6, 36, 8, 22, 14, 6, 48, 10, 6, 6, 30, 8, 6, 36, 4, 20, 46, 44, 40, 14, 46

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 2529 five-digit primes with all distinct digits, so the sequence of differences is finite as well. The end of the sequence is: 42, 18, 80, 42, 30, 10, 38, 22, 38, 22, 30, 38, 162, 28, 2, 18, 156, 24, 6, 10, 66, 20, 64, 6, 38, 6, 60, 4, 6, 20, 60, 46, 14, 6, 34, 36, 18, 2, 10, 48, 6, 14, 72, 18.

			a(1)=4 because the first and second five-digit primes with all distinct digits are 10243, 10247 and difference between them is 4.

Harvey P. Dale, Table of n, a(n) for n = 1..2528 (Complete list of all terms)

The first differences of the A074671. For 3-digit distinct-digit primes, see A074675, A074676. For 4-digit distinct-digit primes, see A074673, A074674. For 6-digit distinct-digit primes, see A074669, A074670. For 7-digit distinct-digit primes, see A074667, A074668. For 8-digit distinct-digit primes, see A074665, A074666.

se=Select[Range[10243, 98731, 2], Length[Union[IntegerDigits[ # ]]]==5&&PrimeQ[ # ]&]; Flatten[Table[{se[[i+1]]-se[[i]]}, {i, 2528}]]
Differences[Select[Prime[Range[PrimePi[10000]+1,PrimePi[99999]]],Max[ DigitCount[ #]] ==1&]] (* Harvey P. Dale, Jul 19 2019 *)

A074674 Differences between successive four-digit distinct-digit primes.

Original entry on oeis.org

10, 14, 6, 18, 6, 4, 140, 12, 10, 20, 4, 6, 8, 10, 20, 40, 42, 14, 4, 2, 10, 14, 6, 24, 4, 2, 4, 30, 20, 6, 18, 12, 4, 14, 10, 2, 18, 10, 20, 36, 4, 12, 14, 30, 6, 24, 6, 34, 24, 20, 6, 6, 28, 66, 14, 30, 22, 14, 10, 6, 12, 2, 4, 2, 48, 6, 10, 26, 130, 32, 6, 4, 6, 14, 10, 8, 28, 20, 22

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 510 four-digit primes with all distinct digits, so the sequence of differences is finite as well.

			a(1)=10 because the first and second four-digit primes with all distinct digits are 1039, 1049 and difference between them is 10.

Harvey P. Dale, Table of n, a(n) for n = 1..509

The first differences of the A074673. For 3-digit distinct-digit primes, see A074675, A074676. For 5-digit distinct-digit primes, see A074671, A074672. For 6-digit distinct-digit primes, see A074669, A074670. For 7-digit distinct-digit primes, see A074667, A074668. For 8-digit distinct-digit primes, see A074665, A074666.

se=Select[Range[1039, 9871, 2], Length[Union[IntegerDigits[ # ]]]==4&&PrimeQ[ # ]&]; Flatten[Table[{se[[i+1]]-se[[i]]}, {i, 509}]]
Differences[Select[Prime[Range[169,1229]],Length[Union[ IntegerDigits[#]]] == 4&]] (* Harvey P. Dale, Oct 11 2015 *)

A073643 Nine-digit primes with all distinct digits.

Original entry on oeis.org

102345689, 102345697, 102345869, 102346789, 102346879, 102346897, 102346957, 102347689, 102348679, 102348769, 102349867, 102354689, 102354697, 102356489, 102356789, 102356987, 102358769, 102358967, 102364859, 102364879, 102365897

Offset: 1

Zak Seidov, Aug 29 2002

The number of distinct-digit primes are finite. E.g. there are exactly 145227 such nine-digit primes from 102345689 to 987654103.

All terms have exactly one "0" because nine-digit zero-less numbers with all distinct digits are divisible by 9. - Zak Seidov, Mar 15 2015

			a(1)=102345689 because 102345689 is the smallest 9-digit prime with all distinct digits.

Zak Seidov, Table of n, a(n) for n = 1..10000

For 3-digit distinct-digit primes, see A074675, A074676.
4-digit distinct-digit primes are in A074673, see also A074674.
5-digit distinct-digit primes are in A074671, see also A074672.
6-digit distinct-digit primes are in A074669, see also A074670.
7-digit distinct-digit primes are in A074667, see also A074668.
8-digit distinct-digit primes are in A074665, see also A074666.

from sympy import isprime
from itertools import permutations as perms
nines = (int("".join(p)) for p in perms("0123456789", 9) if p[0] != "0")
afull = [k for k in nines if isprime(k)]
print(afull[:24]) # Michael S. Branicky, Aug 04 2022

A074676 Differences between consecutive three-digit distinct-digit primes.

Original entry on oeis.org

4, 2, 18, 10, 2, 10, 8, 6, 4, 6, 6, 14, 4, 42, 2, 10, 6, 6, 6, 2, 10, 2, 10, 14, 10, 30, 2, 10, 8, 12, 10, 8, 4, 8, 10, 2, 10, 8, 18, 4, 2, 4, 12, 8, 4, 12, 6, 12, 2, 18, 6, 16, 6, 2, 16, 6, 8, 6, 6, 4, 2, 12, 10, 2, 4, 6, 6, 14, 10, 8, 10, 8, 10, 20, 4, 8, 10, 8, 40, 12, 2, 4, 2, 10, 14, 4, 2

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 97 three-digit primes with all distinct digits, so the sequence is finite.

			a(1)=4 because the first and the second three-digit primes with all distinct digits are 103, 107 and difference between them is 4.

Jinyuan Wang, Table of n, a(n) for n = 1..96

The first differences of the A074675. For 4-digit distinct-digit primes, see A074673, A074674. For 5-digit distinct-digit primes, see A074671, A074672. For 6-digit distinct-digit primes, see A074669, A074670. For 7-digit distinct-digit primes, see A074667, A074668. For 8-digit distinct-digit primes, see A074665, A074666.

se=Select[Range[103, 983, 2], Length[Union[IntegerDigits[ # ]]]==3&&PrimeQ[ # ]&]; Flatten[Table[{se[[i+1]]-se[[i]]}, {i, 96}]]

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A074667 Seven-digit distinct-digit primes.

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A074671 Five-digit distinct-digit primes.

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A074673 Four-digit distinct-digit primes.

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A074669 Six-digit distinct-digit primes.

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A074670 Differences between successive six-digit distinct-digit primes.

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A074675 Three-digit distinct-digit primes.

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A074672 Differences between successive five-digit distinct-digit primes.

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A074674 Differences between successive four-digit distinct-digit primes.

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