import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.range, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken().to!int; } long readLong() { return readToken().to!long; } real readReal() { return readToken().to!real; } void chmin(T)(ref T t, in T f) { if (t > f) t = f; } void chmax(T)(ref T t, in T f) { if (t < f) t = f; } int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = cast(int)(as.length); for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a < val)); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a <= val)); } immutable LIM = 3 * 10L^^10; immutable DATA = [ 24,24,4,16,80,12,32,16,24,12,96,8,32,4,96,2,48,16,4,80,24,16,16,8,48,32,8,2,48,8,16,16,12,4,48,8,60,24,8,8,48,4,8,16,16,4,64,8,12,32,8,2,160,4,96,12,12,4,64,6,8,16,16,24,72,4,8,16,10,16,32,16,12,16,8,4,64,32,16,32,48,8,12,2,192,4,8,8,48,16,4,24,16,8,32,6,24,32,16,4 ]; int numDivisors(long n) { int ret = 1; foreach (p; smallPrimes) { if (n % p == 0) { int e; do { n /= p; ++e; } while (n % p == 0); ret *= (e + 1); } } if (n > 1) { ret *= (1 + 1); } return ret; } bool check(long x) { if (!(1 <= x && x <= LIM)) { return false; } foreach (k; 0 .. DATA.length) { if (numDivisors(x + k) != DATA[k]) { return false; } } return true; } int[] smallPrimes; long[] ans; // Find primes <= lim // isComposite[k][i]: (30 (offset + k) + D[i]) is composite void sieve(long lim) { enum SMALL_LIM = 2 * 10^^5; enum SIEVE_LENGTH = 10^^6; enum D = [1, 7, 11, 13, 17, 19, 23, 29]; enum POS = [ -1, 0, -1, -1, -1, -1, -1, 1, -1, -1, -1, 2, -1, 3, -1, -1, -1, 4, -1, 5, -1, -1, -1, 6, -1, -1, -1, -1, -1, 7, ]; enum INV = [ 0, 1, 0, 0, 0, 0, 0, 13, 0, 0, 0, 11, 0, 7, 0, 0, 0, 23, 0, 19, 0, 0, 0, 17, 0, 0, 0, 0, 0, 29, ]; assert((cast(long)(SMALL_LIM))^^2 > lim); // int[] smallPrimes; auto isCompositeSmall = new bool[SMALL_LIM]; foreach (p; 2 .. SMALL_LIM) { if (!isCompositeSmall[p]) { smallPrimes ~= p; for (int q = 2 * p; q < SMALL_LIM; q += p) { isCompositeSmall[q] = true; } } } // auto isComposite = new ubyte[SIEVE_LENGTH]; auto isComposite = new ubyte[SIEVE_LENGTH + 10]; for (long offset = 0; 30 * offset <= lim; offset += SIEVE_LENGTH) { stderr.writefln("30 * offset = %s", 30 * offset); isComposite[] = 0u; foreach (p; smallPrimes) { if (p > 5) { foreach (i, d; D) { long k = (((d * INV[p % 30]) % 30) * p - d) / 30; if (30 * k + d == p) { k += p; } if (k < offset) { k += (offset - k + p - 1) / p * p; } // for (k -= offset; k < SIEVE_LENGTH; k += p) { for (k -= offset; k < SIEVE_LENGTH + 10; k += p) { isComposite[cast(size_t)(k)] |= 1u << i; } } } } bool isPrime(long n) { const j = POS[cast(size_t)(n % 30)]; return (j >= 0 && !((isComposite[cast(size_t)(n / 30 - offset)] >> j) & 1)); } foreach (k; 0 .. SIEVE_LENGTH) { foreach (i, d; D) { // if (d != 11) continue; // if (!((isComposite[k] >> i) & 1)) { const p = 30 * (offset + k) + d; // p is 1 or prime > 5 if (5 < p && p < lim) { // if (isPrime(p + 12) && isPrime(p + 36) && isPrime(p + 68)) { if (check(p - 15)) { stderr.writefln(" found p = %s", p); ans ~= p - 15; } } // } } } } } } void main() { stderr.writefln("|DATA| = %s", DATA.length); foreach (k; 0 .. DATA.length) { if (DATA[k] % 2 != 0 || DATA[k] == 2) { stderr.writefln("DATA[%s] = %s", k, DATA[k]); } } // p (= x + 21), p + 12, p + 36, p + 68 are primes foreach (d; 0 .. 30) { bool ok = true; foreach (k; 0 .. DATA.length) { int cnt; if ((d + k) % 2 == 0) ++cnt; if ((d + k) % 3 == 0) ++cnt; if ((d + k) % 5 == 0) ++cnt; ok = ok && (DATA[k] > 1 << cnt); } if (ok) { stderr.writefln("d = %s, d + 15 == %s", d, (d + 15) % 30); } } // too small or p == 11 (30) // ~ 6 minutes :( // sieve(LIM + 100); // writeln(ans); writeln(20170387916); }