Today I'm 25463 days old and I can't let it pass without recording some of its more interesting properties. One of these is that it is a member of OEIS A165572: the greater prime factor of successively better Golden Semiprimes. These semiprimes p*q, starting from 6=2*3, have the property that each successive value of q/p gives a better approximation of the Golden Ratio than the previous term where the $$ \text{Golden Ratio } \phi=\frac{1+\sqrt(5)}{2} \approx \, 1.61803398874989$$Here are the initial members of this sequence: 3, 5, 11, 31, 37, 47, 157, 571, 911, 1021, 1487, 2351, 3571, 24709, 25463. The corresponding semiprimes form OEIS A165570 and consist of 6, 15, 77, 589, 851, 1363, 15229, 201563, 512893, 644251, 1366553, 3416003, 7881197, 377331139, 400711231, 2963563859, 4035221017.
Here are the progressively better approximations as the larger factor of the semiprime is divided by the smaller:
3/2 1.50000000000000
11/7 1.57142857142857
31/19 1.63157894736842
37/23 1.60869565217391
47/29 1.62068965517241
157/97 1.61855670103093
571/353 1.61756373937677
911/563 1.61811722912966
1021/631 1.61806656101426
1487/919 1.61806311207835
2351/1453 1.61803165863730
3571/2207 1.61803352967830
24709/15271 1.61803418243730
25463/15737 1.61803393276991
Another property of 25463, albeit a base dependent one, is its membership in OEIS A156119: primes formed by rearranging five consecutive decimal digits (avoiding leading 0). No primes can be formed from {1,2,3,4,5} or {4,5,6,7,8} since they are divisible by three. Sequence is finite, ending with a(52)=96857. Initial members of sequence are: 10243, 12043, 20143, 20341, 20431, 23041, 24103, 25463.
Yet another property, again base dependent, is its membership of OEIS A124629: primes p such that their cubes are pandigital, meaning all digits from 0 to 9 must appear at least once; here 25463^3=16509301927847. The initial members of this sequence are: 5437, 6221, 7219, 8443, 10903, 11353, 15937, 17123, 18229, 19429, 20353, 20903, 20929, 21803, 21841, 21961, 22123, 22283, 22993, 23053, 23369, 23663, 24733, 25183, 25219, 25463.
Not base dependent is the property that 25463 shares as a member of OEIS A226154: smallest of four consecutive primes whose sum is a triangular number. Triangular numbers are of the form:$$ \binom{n}{2}= \frac{n \, (n-1)}{2}$$The initial members of this sequence are: 5, 23, 191, 389, 449, 2593, 3011, 5167, 5639, 5851, 8669, 18839, 25463. Here the four primes add to 101926 = 25463+25469+25471+25523 and this sum is a triangular number because: $$101926 = \binom{452}{2}=\frac{452 \times 451}{2}$$
Finally and again base independently, 25463 is a member of OEIS A022121: Fibonacci sequence beginning 3, 8. The initial members of this sequence are: 3, 8, 11, 19, 30, 49, 79, 128, 207, 335, 542, 877, 1419, 2296, 3715, 6011, 9726, 15737, 25463.
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