Block #320,473

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 4:26:25 PM · Difficulty 10.1838 · 6,497,155 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c1db90a4c3331061550f34e515008fde243810d2743d1073025436a4758800f

View on Chainz ↗

Height

#320,473

Difficulty

10.183761

Transactions

Size

1.64 KB

Version

Bits

0a2f0af0

Nonce

7,580

Timestamp

12/19/2013, 4:26:25 PM

Confirmations

6,497,155

Mined by

⛏️ aRAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

ea4e230df8a09ec5eae0b304ca6f6c218995e2e83b2e04ce911c0069f589aa63

Transactions (4)

Coinbase1e2a17a537029a…b6f9c3e2d49ef5

1 in → 25 out9.6300 XPM913 B

AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG AMbCuLHZ…WSoStwkc ASZ52DiD…cGtaKFzN

b5706e4edecd14…28b976374df660

1 in → 2 out8.6545 XPM225 B

ATdEHjkc…xdoGAvt3 AMt9Df4M…V1apSTFS

a588baa91175ba…37c5b4114e5571

1 in → 2 out8.6556 XPM226 B

Aa2yQGsc…961dv95g ARii5Exz…pwPPaDe6

e292c81f5d479c…0330909a4122e1

1 in → 2 out7.6437 XPM226 B

Ae8UGEc3…6BebZYrL AKtRZmfN…8CR6id6j

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.

8.638 × 10⁹²(93-digit number)

86387560883647193777…69223222505869116359

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

8.638 × 10⁹²(93-digit number)

86387560883647193777…69223222505869116359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.638 × 10⁹²(93-digit number)

86387560883647193777…69223222505869116361

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

1.727 × 10⁹³(94-digit number)

17277512176729438755…38446445011738232719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.727 × 10⁹³(94-digit number)

17277512176729438755…38446445011738232721

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

3.455 × 10⁹³(94-digit number)

34555024353458877511…76892890023476465439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.455 × 10⁹³(94-digit number)

34555024353458877511…76892890023476465441

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

6.911 × 10⁹³(94-digit number)

69110048706917755022…53785780046952930879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.911 × 10⁹³(94-digit number)

69110048706917755022…53785780046952930881

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

1.382 × 10⁹⁴(95-digit number)

13822009741383551004…07571560093905861759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.382 × 10⁹⁴(95-digit number)

13822009741383551004…07571560093905861761

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

Block #320,473

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