I'm assuming you will be using the Arduino millis() function for keeping time. The output of the millis() function in the Arduino environment is a 32-bit unsigned integer*.

A 32-bit integer can be split into 4 x 8-bit bytes. To keep things simple you could program the Java receiving side to always expect 4 bytes (or whatever amount you need, see *). Assuming 32 bits is enough, you could use the following:

void sendData (uint32_t uptime) {
    int i;
    for (i = 0; i < 4; i++) {
        Serial.write (uptime & 255);
        uptime = uptime >> 8;
    }
}

On the Java side, you would receive the lowest order byte first, and you could reconstruct the 32-bit value by taking the first received 8-bit value, adding the second value shifted left by 8 bits (=multiplied by 256), adding the third value shifted left by 16 bits (=multiplied by 65536) and adding the fourth value shifted left by 24 bits (=multiplied by 16777216). Java is not my strong point so I will leave that to you.

*After 2^32 milliseconds (a bit over 50 days of uptime) the 32-bit counter that feeds the millis() function will wrap around to 0. You could keep the amount of times that the timer has overflowed in a separate (integer) variable and make that (i.e. bytes 5 and onward) part of your output.

I'm assuming you will be using the Arduino millis() function for keeping time. The output of the millis() function in the Arduino environment is a 32-bit unsigned integer*.

A 32-bit integer can be split into 4 x 8-bit bytes. To keep things simple you could program the Java receiving side to always expect 4 bytes (or whatever amount you need, see *). Assuming 32 bits is enough, you could use the following:

void sendData (uint32_t uptime) {
    int i;
    for (i = 0; i < 4; i++) {
        Serial.write (uptime & 255);
        uptime = uptime >> 8;
    }
}

On the Java side, you would receive the lowest order byte first, and you could reconstruct the 32-bit value by taking the first received 8-bit value, adding the second value shifted left by 8 bits (=multiplied by 256), adding the third value shifted left by 16 bits (=multiplied by 65536) and adding the fourth value shifted left by 24 bits (=multiplied by 16777216). Java is not my strong point so I will leave that to you.

BTW, is there a particular reason you have to use Serial.write()? It would be much easier to just write the value as a string with Serial.println().

*After 2^32 milliseconds (a little under 50 days of uptime) the 32-bit counter that feeds the millis() function will wrap around to 0. You could keep the amount of times that the timer has overflowed in a separate (integer) variable and make that (i.e. bytes 5 and onward) part of your output.