27523 (and the previous number 27522) have the property that all their digits are prime and so they are members of OEIS A046034.

There are 852 such numbers in the range up to 40000 with 124 of them being prime (the next one being 27527). Permalink.

The remaining 27**** numbers are:

27522, 27523, 27525, 27527, 27532, 27533, 27535, 27537, 27552, 27553, 27555, 27557, 27572, 27573, 27575, 27577, 27722, 27723, 27725, 27727, 27732, 27733, 27735, 27737, 27752, 27753, 27755, 27757, 27772, 27773, 27775, 27777

After 27777, the next member of the sequence is 32222.

27523 has the property that starting with 2 and 7 as seed digits, the subsequent digits can be generated by the absolute value of the two previous digits. Thus 7 - 2 = 5, the third digit, and 7 - 5 = 2, the fourth digit, and 5 - 2 = 3, the last digit. See blog post Subtractive Fibonacci-like Numbers.

27523 has 420 as its product of digits and we find that

• 27523 + 420 = 27943 which is a prime number
• 27523 - 420 = 27103 which is a prime number

27523 is a happy, cyclic, Duffinian and self number.

27523 can be rendered as a digit equation as follows:

(-2 + 7) / 5 + 2 = 3