How long would it take Earth's fastest space ship to reach Proxima Centauri?

To date, humans have launched only four space probes that will eventually leave the solar system. These vehicles will likely travel across the depths of space for millions of years to come. NASA launched all four of these remarkable craft during the 1970s to make the first close-up studies of the gas giants in the outer solar system. Following their historic visits to our largest planetary neighbors, the four vehicles followed paths that will carry them beyond the edge of the solar system and into interstellar space.

The first of these space probes was Pioneer 10 that was launched in 1972 and visited Jupiter a year later. Pioneer 10 is currently traversing what we believe to be the edge of the solar system. Unfortunately, the vehicle's power source, a Radioisotope Thermoelectric Generator (RTG), has decayed to the point that it can no longer provide enough electricity to operate the probe. Pioneer 10 stopped transmitting signals to Earth on 23 January 2003 when the craft was over 7.6 billion miles away. The trajectory of Pioneer 10 will bring the vehicle close to the star Aldebaran in the constellation Taurus (The Bull) in about 2 million years.
A twin spacecraft named Pioneer 11 also visited Jupiter in 1974 and continued on to make a flyby of Saturn in 1979. Pioneer 11 too is now on its way into deep space as it heads towards the constellation Aquila (The Eagle). The spacecraft should pass close to one of the stars in that constellation in about 4 million years. Pioneer 11 has also stopped transmitting to Earth, and its final signal was received in November 1995.
Two more NASA probes that built on the successful missions of Pioneer 10 and 11 were the Voyagers. Voyager 1 also visited Jupiter and Saturn and is presently sailing towards the outer limits of the solar system. The craft is headed towards the constellation Camelopardalis (The Giraffe), a star of which it will fly close to in about 300,000 years. Voyager 2 flew past Jupiter, Saturn, Uranus, and Neptune during its Grand Tour of the solar system, but the probe is now headed towards the star Sirius in the constellation Canis Majoris (The Big Dog). Sirius is the brightest star in the night sky, and Voyager 2 will pass close to it in about 160,000 years. Both of the Voyager probes are still transmitting and are expected to continue sending signals to Earth until around 2020 when their power sources decay.

The two Voyagers will be over 10 billion miles from the Sun by then, and it is hoped they will provide the first scientific measurements of the edge of the solar system and the beginnings of interstellar space. The prevailing theory accepted by most researchers says that the edge of the solar system consists of three boundaries called the termination shock, heliopause, and bow shock. The termination shock is believed to mark the transition in the velocity of the solar winds emanating from the Sun from supersonic to subsonic speeds. Even further away is the heliopause, which scientists conjecture is a region where the solar wind ceases to exist. Beyond may lie a bow shock bombarded by galactic cosmic rays. However, these theories of the solar system's outer reaches remain unproven. Only the Voyager probes may be able to provide scientists with any answers about the true nature of this region of space anytime soon.
All four of these distant space probes used the gravitational attraction of the planets they visited to slingshot themselves onto the trajectories they currently follow. These gravitational assists accelerated the vehicles to some of the highest speeds ever reached by manmade objects. Traveling slowest of the foursome is Pioneer 11 at about 26,000 mph (42,000 km/h) with respect to the Sun. Pioneer 10 is currently moving at a rate of over 27,000 mph (44,000 km/h) while Voyager 2 is speeding along at about 36,000 mph (58,000 km/h). The fastest probe, however, is Voyager 1 with a velocity of nearly 39,000 mph (63,000 km/h). Given its greater speed, Voyager 1 currently holds the record as the fastest interplanetary spacecraft and has passed the Pioneers to become the farthest manmade object from the Sun.
None of these four spacecraft is traveling towards our closest star Proxima Centauri that lies about 4.2 light years away. If Voyager 1 were headed in that direction, however, it would still take the vehicle over 73,000 years to get there!

Helios

The Helios, which holds the record for fastest manmade object, was a series of two spacecraft launched in the mid-1970s to study the Sun. Both probes were developed through cooperation between the US and West Germany with scientists from both nations providing experiments and NASA providing the launch vehicle and booster. Helios 1 was launched in December 1974 and Helios 2 in January 1976, both reaching the Sun within about three months.

What made the Helios missions so unusual was that the two craft made incredibly close passes to the Sun resulting in very high orbital speeds. These high speeds resulted from the fact that both probes were placed into very elliptical, or eccentric, orbits around the Sun. When a probe is placed into a circular orbit, its speed remains a constant. For example, the Space Shuttle orbits the Earth in a circular or nearly circular orbit at a constant speed of between 17,000 and 18,000 mph (27,355 to 28,960 km/h). When in a highly elliptical orbit, however, a vehicle will reach very high speed when it is close to the body it is orbiting but slow down considerably when it is far away.
The Helios missions both orbited in this manner, with a furthest distance (or aphelion) of nearly 1 Astronomical Unit (AU), which is the distance at which the Earth orbits the Sun. Meanwhile, the closest approach (or perihelion) of the Helios probes was about 0.3 AU. The eccentricity of such an orbit is about 0.54 with a period of about 190 days. The maximum speed of Helios 2, which achieved its perihelion distance of 0.29 AU on 17 April 1976, is quoted as about 150,000 mph (241,350 km/h). By applying some simple equations of orbital mechanics, we can confirm that such an orbit would indeed result in a perihelion velocity of 153,800 mph (247,510 km/h). For comparison, the aphelion speed of Helios 2 turns out to be only 45,360 mph (72,985 km/h) at its farthest distance of 0.983 AU. This massive differential between the vehicle's maximum and minimum speeds graphically illustrates how much an elliptical orbit varies from the circular orbit discussed earlier.
The reason the Helios probes were given such unusual orbits is that they were intended to make various measurements of the interplanetary space between the Sun and Earth. Each probe was equipped with ten experiments including high-energy particle detectors to measure the solar wind, magnetometer readings of the Sun's magnetic field, measurements of variations in electric and magnetic waves, and a micrometeoroid experiments. The two probes completed their primary missions by the early 1980s but were still sending data as late as 1985. Though they are no longer functional, both craft remain in their eccentric orbits around the Sun.