Block #482,733

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 4:04:19 PM · Difficulty 10.5506 · 6,313,872 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

50e54e40047166a27d1b546c3c33bc964958b5d909bb89e6f13a340e45613011

View on Chainz ↗

Height

#482,733

Difficulty

10.550560

Transactions

Size

3.40 KB

Version

Bits

0a8cf186

Nonce

134,183

Timestamp

4/9/2014, 4:04:19 PM

Confirmations

6,313,872

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

79a89acdaadf857d1f3f4051d464148be1b0e93d8f17cad3df073de46e97d7c4

Transactions (5)

Coinbased73ca548985450…c3d9c188f52baa

1 in → 1 out9.0300 XPM116 B

AbwWkWZt…kawDhufa

1ee8db9da971b6…f5696738c13374

8 in → 37 out72.5400 XPM2.39 KB

AUkdqaxr…4jcbMUQ7 ASqqpxAv…dTvgfRnF ATvxvGPc…EyBahBRQ AKzv8KjF…W6FeM9j1 ALgG3mZQ…bxBpBADL

a57769eed8cc74…d3181014c2065e

2 in → 2 out5.5978 XPM374 B

ASaCaMjW…pndnMiEC Ad8GrTrQ…2jA9ArGd

7c75fbfa9b4bc8…834b0b655e286c

1 in → 2 out3.8745 XPM226 B

ALNxWiU6…YrgSSXK4 AMXY8SA8…apkQS381

ebc579294782f5…7f9310913d94b2

1 in → 2 out4.4442 XPM227 B

AbfHauC7…MoRHCkNL AQmsxaYz…dqsWkDMW

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.317 × 10⁹⁸(99-digit number)

23179105317616588047…21419352058064071359

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.317 × 10⁹⁸(99-digit number)

23179105317616588047…21419352058064071359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.317 × 10⁹⁸(99-digit number)

23179105317616588047…21419352058064071361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.635 × 10⁹⁸(99-digit number)

46358210635233176094…42838704116128142719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.635 × 10⁹⁸(99-digit number)

46358210635233176094…42838704116128142721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

9.271 × 10⁹⁸(99-digit number)

92716421270466352188…85677408232256285439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.271 × 10⁹⁸(99-digit number)

92716421270466352188…85677408232256285441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.854 × 10⁹⁹(100-digit number)

18543284254093270437…71354816464512570879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.854 × 10⁹⁹(100-digit number)

18543284254093270437…71354816464512570881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.708 × 10⁹⁹(100-digit number)

37086568508186540875…42709632929025141759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.708 × 10⁹⁹(100-digit number)

37086568508186540875…42709632929025141761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer