A new birding lens for my Nikon.

[Cage]

As the title suggests I'm looking at a new long distance lens, initially on the D7200 and possibly on a D750.

Due to the size of my budget, the big primes are out of the equation, and I've narrowed the contenders down to three, the Nikon 200-500mm f5.6 ED VR, the Tamron SP 150-600mm F/5-6.3 G2 Di VC USD and the Sigma 150-600mm F5-6.3 DG OS HSM Sport.

I've looked at heaps of comparisons and the following observations seem to be constant.

IQ: No stand-out winner but at 500mm, the Nikon by a smidgeon.

AUTOFOCUS: The Nikon again, with the VR giving the most stable image in the viewfinder.

VR/VC/OS: Once again pretty even

1.4 T/C COMPATIBILITY: for the Nikon, a bit hit and miss with the other two

FOCAL LENGTH: Longer is better, right? However most testers commented that the long end of the Tamron and Sigma was nearer to 550mm than 600mm and both lost some IQ @ 600mm Hmmmm.

WEATHER SEALING: Tamron, tick, Sigma, tick, Nikon, no mention, although you can get a waterproof camo cover for about thirty bucks.

MOUNT: Tamron, with it's Arca Swiss foot, the Sigma and Nikon a bit iffy, but not enough to be a deterrent.

UPGRADES: The Sigma and Tamron, with their docks, have a big advantage. The Nikon has already had firmware updates which requires the lens to be sent back to Nikon involving postage cost and time without the lens.

BRAND LOYALTY: I have the Nikon AF-S 300mm f4, a cracker of a lens which I'll keep, whatever I decide on, the Sigma 150mm f2.8 Macro, cut ya' finger sharp, and the Tamron twins, the 24-70 and the 70-200 f2.8's, both exceeded my expectations, so I'd be delighted if the 150-600 was in the same league.

WEIGHT: T - 1990g: N - 2300g: S - 2860g Not really a factor as I'd do little hand-held shooting

PRICE: Depending on when, and where you look, the price seems to increase in line with the weight, with the Tamron the cheapest, the Nikon a bit dearer and the Sigma a bit dearer again.

VFM: The Tamron looks the best Value For Money with it's weather sealing, Arca Swiss lens foot and tap-in colsole.

BEST FOR ME: This will be my birding lens and as you birders know you often only have a couple of seconds to find the subject, get focus, stabilise, and take the shot. The Nikon generally seems to do this a tad better than the other two.

There really is not a great deal between the three lens and I guess it comes down to how they each fit your particular needs, likes and dislikes. I think I'd be pretty chuffed to own any one of them.

I'm still undecided so any pertinent comments appreciated.

[J.davis]

I have the Sigma C lens and am very happy with it, bloody sight cheaper too.

[arthurking83]

You probably already know of my anti-Nikon bias already .. and until they prove that they have made changes to their customer relations ethics, I refuse to recommend their products if an alternative exists.

Having said that tho, Those geeky docks are handy to play with, so recommendations come highly. Some folks see them as insurance for thirdparty incompatibility issues, I see it as a way to tailor the lens to suit your need.
ie. if you want faster focusing, and less emphasis on accuracy, you choose to tweak it as such. if you prefer more accurate, and less speed, then tweak it that way. The point is, you get to choose how it works for 'ya.

Note too tho, this doesn't mean that the lens is necessarily slow focusing or inaccurate at doing so .. it's that you get fine degrees of flexibility at either option.

I can only offer user based comments on the Sigma Sport lens, and offer a very good summary for it.
Can't be faulted, other than the stupid lens hood design. And even that negative comment is just me being pedantic!
The lens hood uses a screw in/out locking tab that is just plain annoying to have to use.
Instead of a full screw in/out system, they should have used a half turn screw to unlock it, then a spring loaded pull system that allows quicker removal and reversal of the lens hood.

Optically, I can't imagine you'd complain about it.
Obviously you wouldn't compare it's resolving power against a prime lens of the same focal lengths, but the comments re it's ability at 600mm are 'overstated' IMO.
The bigger issue at longer focal lengths is always going to be user technique. Be that hand held or even on a tripod.

Focusing speed on a D800E and D300 hasn't given me any cause for concern .. but I've yet to try a Nikon 200-500 lens either.
Other than the Nikon 70-200/2.8 lenses I've occasionally tried, I can't really think of any lens that really focuses all that much faster.
Accuracy in 'everyday' use will come down to what your everyday usage actually is.
Teeny birds hiding in amongst twigs and branches .. lens may hunt .. ie. as in the camera may struggle with the distractions!

If the subject is out in the clear .. like a cocky would roost on the highest point out in the open on a bare tree limb .. focus is fast and accurate.

At the apertures you're most likely to be shooting at, I don't think the f/6.3 apertures will be an issue for you.

[Tannin]

G'day Kev,

I know little about the Nikon lenses so I can only make some comments on side issues.

On focal length, the very reliable Bryan Canathan (The Digital Picture) provides actual focal length estimates for the Sigma and the Tamron by comparing them to a Canon 600/4 prime. On that basis, he puts the Tamron at around 570mm and the Sigma at roughly 555mm.

The Digital Picture does not review Nikon lenses and after a quick search I couldn't find an equivalently authoritative source for the 200-500 focal length. In this DPR thread https://www.dpreview.com/forums/thread/4022958 a poster compares his 200-500 to a Nikon 500/4 prime and claims the zoom is only about 460mm but I'm not convinced that he's measured it accurately - in particular, he does not state the distance to subject and you really must measure focal length at (or at least near) infinity. As I recall (source long since forgotten) even the big super-tele primes understate their actual FL by a small margin, meaning that figures for zooms calculated by comparison to a 500/4 or 600/4 will be a little lower still, but that need not concern us as we all know what to expect from a "500mm" prime.

TDP measures the Canon 100-400 Mark II at 383mm compared to the Canon 400/5.6 and 400/2.8; the old Canon 100-400 is similar. There is a clear pattern from all these measurements, and it would be surprising to discover the the Nikon 200-500 was not somewhere around about 475mm actual.

I'm a big fan of fast AF for birding, and even a small difference is a big difference, in my view. I'm always a bit skeptical about f/6.3 lenses. They work fine, but regardless of your shooting aperture all else being equal, a bigger hole in the glass is always better.

To me, the fact that the Sigma and the Tamron require upgrade and adjustment docks is a clear disadvantage. Obviously, you have to factor in the (not insubstantial) cost of the dock if you don't already have one. But more importantly, it says to me that the Nikon lens does not need a dock to ensure proper function and compatibility with future Nikon cameras. It will just work. I know that Canon go to a great deal of trouble testing new cameras and teleconverters and so on with all possible lenses going back many years to ensure compatibility, I'd be very surprised to discover that Nikon didn't do the same.

The Sigma is a massive, awkward lump of a thing. I know you say you wouldn't hand-hold much - well, if you owned the Sigma, you wouldn't! At 2.3kg, the Nikon is no lightweight either; nevertheless, half a kilogram in your hand or on your shoulder is a very significant difference.

Of those three, my choice would probably be the Nikon. Indeed, I have recently made a rather similar choice in deciding to upgrade my Canon 100-400 Mark 1 to the Mark II rather than to the Sigma or the Tamron. In my case, however, weight, hand-holdability, and AF speed were more important than focal length as I already have a 500/4 for tripod work. Also, the wide end is important as I don't own a 70-200 or 70-300 and I use the 100-400 a lot as a "poor man's 70-300" for landscape and other non-birding tasks.

That said, the Sigma is certainly a very competent birding lens - I refer you to the consistently excellent work Mark L does with his. I happen to know that a member here (not Mark) is planning to sell his as-new condition Sigma 150-600 shortly, so if you are leaning in the Sigma direction, that might be something to bear in mind.

[Cage]

@ Artie ....

You probably already know of my anti-Nikon bias already .. and until they prove that they have made changes to their customer relations ethics, I refuse to recommend their products if an alternative exists.

Many thanks for your comprehensive reply Artie. My only dealing with Nikon was with my D600 shutter replacement, and that went seamlessly.

My major concern is with QC as the term 'sample variation' came up all too frequently in tests for all three candidates. If I buy a cheap Chinese knock-off of anything I expect 'sample variation' and dodgy QC, but not in a $1500+ lens. Hell, that's about 10% of the price of a new compact car that also has software controlled functions and if they worked as well as those in camera lens there would be a new nouveau rich group, panel beaters ! Gawd, I hope the self drive cars are using better technology to decide when to apply the brakes, although it is probably some sort of radar gizmo.

Mate, I'm glad you are happy with your Siggy. It seems to be a well regarded bit of kit.

@Tony....

Appreciate you taking the time to assist with your inciteful reply.

My birding kit will generally be the D7200 with it's high pixel density and good high ISO performance. When using a tripod (Manfrotto 055CXPRO3) I mount my Wimberley Sidekick on a Markins ballhead, and where possible use a remote release. The Sidekick is the best bit of mounting hardware I have. With a long lens-plate I can balance my kit perfectly, and it is so well engineered that it has a 'sweet spot' where you lock it and it won't droop, but still allow easy vertical adjustment, with the horizontal adjustment being looked after by the ball-heads panning base. Works for me with my less than steady hands.

With the D7200's 1.5 crop factor my FOV @600mm is 900mm FX equivalent, so realistically I don't feel the loss of 75mm is going to be a huge factor. What will be the big learning curve, IMHO, will be adjustiing my shooting distance and focus points. If you look at the DOF snip below, at 10m even Weebill's are going to be a challenge unless they are side-on.


DOF 800mm.JPG


I really want to get excited about the Nikon but it's not happening. LanceB has posted some great shots with his on a D500, with it's great auto-focus capability, but poor mongo got one with, I think, some out of alignment lens elements. It shouldn't be, but I guess that's a possibility with which ever one I choose, and for that reason I won't consider a pre-loved unit.

In my search of comparisons there does not seem to be a clear stand-out between the three, with various commentators subjectively giving one a slight nod over the other two. I think that they would all please me.

At this point I'm leaning toward the Tamron, although the new Aussie distributors trading name, Blonde Robot, is less than confidence inspiring. I came across this reviewer that may be influencing my decision a tad. https://photographylife.com/reviews/...00mm-f5-6-3-g2 Only one persons opinion, but seemed to know what he was talking about and did not seem biased at all.

I think the Tamron ticks the most boxes for me, and from my experiences with their 24-70 and 70-200 I have a good idea of what to expect from their product.

Decisions, decisions !!

[Cage]

The two Tamrons I have I bought from Teds at not much more than Grey Market price.

The new distributor, Blonde Robot, has obviously decided to go the greedy route, and Tamron's current pricing is now 40% above the Grey Market price.

I HATE PRICE GOUGING !!!!

So on principle I'm scrapping the Tamron. Plus it's now about three hundred bucks dearer than the Nikon.

[jim]

I've got the old version of the Tamron and it's an excellent lens. It's also much better at 600 than the reviews had led me to believe (or it would be if it really went to 600. It's shorter at 600 than the 200-400 f4 is at 400 with a 1.4x teleconverter, which I think is taking the piss a wee bit.)

[Mark L]

To me, the fact that the Sigma and the Tamron require upgrade and adjustment docks is a clear disadvantage. Obviously, you have to factor in the (not insubstantial) cost of the dock if you don't already have one.

Maybe the docks are an advantage to allow you to do fine tuning without having to pay for some one to fix the slight front focusing your lens may have. Let's hope you don't need that with the Nikon lens.
I suspect I know a member here that would lend a dock if needed (not me, but if needed let me know).
I've not seen the Sigma required any upgrades?
AF speed with the Sigma is pretty good. If you have some detail infinity to minimum focal length in less than a secound with my 80D.

[KevPride]

I have the 200-500 f5.6 and have used on a d7100 and d500, I see no reason to part with it for either of the other lenses which were available when I got the Nikon last year. I hand hold the Nikon with ease.

[Tannin]

Maybe the docks are an advantage to allow you to do fine tuning without having to pay for some one to fix the slight front focusing your lens may have.

I must admit that I have never yet owned a lens - and I've had a few - that didn't focus correctly out of the box. (However I admit that I've only had three non-Canon lenses. Still got one of them: Tokina fisheye zoom. Lovely little thing.)

[arthurking83]

I'd have to say, I enjoy the layout of TDP myself too, and seeing his lens results gives a sense of destiny placed in your own hands.
(ie. by that, I'm referring to the point that you view the test target images for yourself, and you believe what you want to see, and make your own choice).

So for me, not only did I have a slight bias against Nikon's lenses to begin with, the images of both the Sigma C and S lenses both displayed more clarity and contrast than the Nikon 200-500 lens.
Using that hair brained rationale, the Sigma(s) were a no brainer .. just a matter of which one. I think I saw just enough extra IQ quality in the S model to justify it's extra cost and weight(and size!!) to warrant the effort it'd need by comparison.

So: if you pull up TDP, (and as example) set the the main window to view image quality results of the Sigma lenses, and then for the lens to compare against to be the Nikon lens, firstly, the camera to choose for the Sigma lens should be the 1 Ds III, and for the Nikon lens the camera body should be the D3x. In choosing those camera bodies, you give the Nikon a slightlyu unfair advantage in that the 24Mp of the D3x shows slightly greater detail magnification than the 21Mp of the 1Ds III can display.

Yet!!... the Sigma(s) clearly resolve more contrast detail than the Nikon lens does. (note that if you choose the D810, the Nikon lens then displays more detail but it's contrast level is still inferior. As you well know, that's what those extra pixels do for resolving power!
Another thing that turned me off the Nikon lens, harks back to the Nikon 105VR(macro lens) for me ... that is it's level of CA.
As soon as I noticed those 500mm sample shots of the test target and all that Magenta and Cyan fringing ripped my eyeballs out of their sockets ... I knew this lens wasn't for me(again) .. once bitten twice shy kind'a thing

One other thing to note(back on TDP). if you decide that the Sigma lenses sound 'better' once again check the results of both lenses, and as you say you also want the 1.4x TC, TDP tests both lenses at 840mm with the Sigma 1.4x TC(model 1401).
The Sport lens clearly out performs the C lens with the TC attached ... and useful results will only be found at f/11. set to f/8(wide open) displays only mush from both lenses. At f/11, you can see useful detail from the S lens. Not so much from the C lens.

BTW .. they also test the lenses with the Sigma 2001 model 2x TC .. and well the results speak for themselves!


But the more definitive test results come from Lens Rental.
if you had Canon camera bodies .. the issue wouldn't even come to a head .. the no brainer answer is you'd just get their 100-400, as at 400mm, it out resolves them all.

Between the Nikon 200-500, Sigma 150-600C, and Tamron 150-600 lenses. the pecking order in terms of MTF is Sigma, Nikon and Tamron.
In the MTF charts the graphed value you want to look at for 'sharpness' detail is the purple 50lpmm curve.

Lens Rental's MTF(or sharpness) results is important because they don't measure a lens of each. They measure a minimum of 10 copies of each lens type, to give an averaged result.
So there may be one of each lens brand that is more exceptional in terms of outright performance against the other brands, but the chances of an individual getting that particular lens is 1 in 10.
So understanding that the average results they post, simply means that in a batch of lenses out there in some store at any one time, chances are that the Sigma lenses could be just that little bit more of a sure bet vs the Nikon, vs the Tamron lens.
Another important point from the Lens Rental tests of the Nikon/Tamron/Sigma lenses, was simply that the differences in IQ are so small, they'd barely register a comment one way or the other.
If you're happy with what your Tamron captures, you'd be equally happy with what both the Nikon and Sigma lenses also achieve for 'ya too.

So using TDP's image results, and Lens Rentals averaged results .. I feel 'more justified' in that choosing the Sigma was going to be less of a hassle to get a lens that gave sharp results.
other user's thoughts re the handling of the Sigma lenses also weighed in, and all claimed fast AF and accurate(+ the geeky nature of the dock thingy).

A few months after I had mine(and very little use mind you), Sigma did have a firmware update for the S lens, but only for a 'faster AF performance algorithm' update. It was my choice to use it or ignore it .. I loaded it.

A side note on Lens Rentals testing results on the 400mm shootout too!
They had a major issue in keeping the much heavier Sigma Sport lens steady as they tested it on their machine. They didn't post any results for that lens due to this vibration affecting IQ.
it is a heavy lens .. and I think this finding by Lens Rental may be important in some respects.

I'm not getting a lot of time to get out and play with any of my photography equipment lately. I try every now and then, but it's all too little and far between. So I'm not really in a good position to offer a genuine thorough assessment other than maybe a few hundred images shot with my Sigma.
AF is fast, IQ is good, handholding is hard(heavy) .. lens is heavy .. front heavy! ... it's a bit of fun learning something new. I've never been much into birding other than when out in a group environment.
Strangely, I find I don't have the patience to chase birds for more than about 20-30mins, but I have plenty of patience to sit and wait for the best moment for a landscape shot!

[Cage]

OK, I think it's time to try and rationalise why I think I need one of these lens.

My current birding lens is the Nikon AF-S NIKKOR 300mm f/4D IF ED, with it's always attached TC-14E II. The T/C doesn't seem to have any detrimental affect on IQ so this gives me a very sharp 420mm f5.6 lens, or 630mm f5.6 equivalent FOV on the D7200.

But I always feel that I need more reach, as sometimes you just can't get any closer to your subject.

So comparing what I have to the Nikon 200-500mm f5.6, I find that, allowing for about 5% focus breathing, I have a 475mm f5.6, so I'm only gaining 55mm

What about a T/C? From reports I've read, my current TC-14E II hunts a fair bit on the 200-500, and the TC-14E III (not enough change from $600.00 to buy a schooner) doesn't get the same glowing reports as my current set-up. Added to the fact that the only weather sealing is a gasket on the mounting face, I really don't see that I am gaining very much with this option.

The three 150-600's are, once again allowing a 5% deduction for focus breathing, going to deliver me 570mm, or 855mm equivalent on my D7200, a 36% increase over what I have now, which make the upgrade much more palatable.

From the point of view of IQ, all four are pretty comparable with no real stand-out, so that won't be a deciding factor.

But the fact that they are all dust pumps will. Living in a farming environment, with open-cut coal mining all around, dust is a fact of life so proofing against it's ingress is a very valid consideration for me.

The Sigma C has a "Dust proof and splash proof mount" .... so a gasket on the mounting face ?

The Sigma S has "Dust and splash-proof construction" .... no further elaboration, so one can only assume it's some additional sealing on the lens barrel

The Tamron G2 has "For greater protection when shooting outdoors, leak-proof seals throughout the lens barrel help protect your equipment."

So, it's down to the Tamron and the Sigma S.

The Sigma is 560g heavier, so one could assume that it is better built, and about $1 per gram dearer, $2499 for the Siggy and $1899 for the Tammy, before negotiating and price matching. Does the extra weight and cost make the Sigma a better lens. According to all the reviews I've read, not necessarily.

Seems like I'm back to the Tamron again. I do understand that a lot of the difference in the price to the GM offerings is to cover the local warranty. It's also comforting to know that if I do happen to get a dud I can get it replaced or fixed without having to haggle with someone overseas whose first language is not English. I've had enough of that crap with Telstra. And I really should look at my two previous Tamron purchases as having a win, and not as having a loss in this instance.

Decision time !! I can make this changeover happen fairly quickly, IF I can convince myself to sell my Nikon AF-S NIKKOR 300mm f/4D IF ED + the Nikon TC-14E II. It's such a sharp combo that I'd be gutted if the new lens wasn't as good, although I've nothing but praise for the other two Tamrons that I have.

What to do ????

[Tannin]

Kev, I spend most of my photography time in the deep outback: deserts and near-deserts. Dust is a fact of life for me. I used to have frequent trouble with dust on sensors. (This was back in the day before self-cleaning sensors came along.) In fact, sensor dust was one of the two or three main reasons I switched from being a one-body man to a two-body man: simply to avoid lens swaps in constantly dusty environments. (And then a three-body man. Sigh. After that the rot set in and I got a bit carried away. These days I have take medication for the problem and have trimmed myself back to a mere four at any one time. I can handle it. I can stop any time I like.)

Um ... as I was saying, dust used to be a big problem, but I seldom give it a thought these days. I honestly can't remember the last time I had to clean dust of a sensor. Years, certainly. Granted, most of my lenses are weather-sealed, but the 100-400 certainly isn't, and although I generally dedicate one camera to the 500/4, I still remove the lens frequently to add or remove a teleconverter. The EF 100-400 is notorious among Canon users (at least the sort that post on Internet fora) for being a "dust pump". They whinge and moan about it the way a dog whinges if you leave him tied up and alone all day.

What actual effect does the dust the 100-400 "pumps" have on picture quality? None. Nada. Zip. Nil. Zero. The theory tells us that any reasonable amount of dust inside the lens makes practically no difference. I've owned two different 100-400 "dust pumps", used one or the other of them under harsh, dusty conditions for ... er ... 12 years now, taken tens of thousands of pictures with them. Lens dust is a non issue.

Dust on your sensor is the only dust you have to worry about - 'cause that does impact image quality - and with modern sensors, that's pretty much a non-issue too.

Do you remember that famous Lens Rentals article where they tested a lens with a massive great crack in the front element? It really made the point.

[Mark L]

So with the Sigma S.
First is the full photo. I could get closer with the second but you get the idea. (and minimal PPing here as that is my way).

IMG_7820a.jpg

IMG_7820aa.jpg

[Tannin]

^ I suppose this is a tactless time to be talking about great big bills .... but I love that great big bill!

[Cage]

Kev, I spend most of my photography time in the deep outback: deserts and near-deserts. Dust is a fact of life for me. I used to have frequent trouble with dust on sensors. (This was back in the day before self-cleaning sensors came along.) In fact, sensor dust was one of the two or three main reasons I switched from being a one-body man to a two-body man: simply to avoid lens swaps in constantly dusty environments. (And then a three-body man. Sigh. After that the rot set in and I got a bit carried away. These days I have take medication for the problem and have trimmed myself back to a mere four at any one time. I can handle it. I can stop any time I like.)

Um ... as I was saying, dust used to be a big problem, but I seldom give it a thought these days. I honestly can't remember the last time I had to clean dust of a sensor. Years, certainly. Granted, most of my lenses are weather-sealed, but the 100-400 certainly isn't, and although I generally dedicate one camera to the 500/4, I still remove the lens frequently to add or remove a teleconverter. The EF 100-400 is notorious among Canon users (at least the sort that post on Internet fora) for being a "dust pump". They whinge and moan about it the way a dog whinges if you leave him tied up and alone all day.

What actual effect does the dust the 100-400 "pumps" have on picture quality? None. Nada. Zip. Nil. Zero. The theory tells us that any reasonable amount of dust inside the lens makes practically no difference. I've owned two different 100-400 "dust pumps", used one or the other of them under harsh, dusty conditions for ... er ... 12 years now, taken tens of thousands of pictures with them. Lens dust is a non issue.

Dust on your sensor is the only dust you have to worry about - 'cause that does impact image quality - and with modern sensors, that's pretty much a non-issue too.

Do you remember that famous Lens Rentals article where they tested a lens with a massive great crack in the front element? It really made the point.

Tony, it's not the dust, per se, it's the other stuff that comes in with it, like the dreaded fungi spores. I've already lost one zoom, that I bought new, because of fungus.

[Tannin]

^ Ouch!

I dare say you have considered a dry cabinet?

[Cage]

^ Ouch!

I dare say you have considered a dry cabinet?

Not only considered, but acquired.

[arthurking83]

And maybe some kind of UV light to help kill off any spores.

Oh! .. and I remember you said you want a 1.4x TC to go with the new lens you acquire.
Does that mean you're going to use the TC you have, or that you're going to budget in a new TC to go with it?

I'd recommend that if you go with the Sigma, get the Sigma (TC1401).
Also if you go for the Tammy, then go for Tammy's 1.4xTC (TC-X14).

[Cage]

And maybe some kind of UV light to help kill off any spores.

Oh! .. and I remember you said you want a 1.4x TC to go with the new lens you acquire.
Does that mean you're going to use the TC you have, or that you're going to budget in a new TC to go with it?

I'd recommend that if you go with the Sigma, get the Sigma (TC1401).
Also if you go for the Tammy, then go for Tammy's 1.4xTC (TC-X14).

The T/C was really only a consideration with the Nikon. As the D7200 will be my go-to birding lens, the crop factor will be a big bonus @600mm.

I must confess that the Sport was always my first choice, but being a tight @rsed OAP I was looking for a cheaper alternative. Although the G2 seems to tick the same boxes, my gut feeling is that the Sport is just that tad better so I've requested a 'price match' on it. Be interesting to see what they come back with.

The top item on my birding bucket list is the Wedgie, so shooting with anything less than 600mm would be an exercise in frustration.

So the 300mm f4 has to go, and that decision was made a bit easier when reading Brad Hill's blog re his comparison of the Sigma vs Nikon 500mm f4's. He commented that at 500mm and f8 the IQ with the Sport was comparable with the two primes.