Block #327,283

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 10:54:18 AM · Difficulty 10.1761 · 6,482,519 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

926c616422af02e28a6d2a80cca0c9830cfc92d745396d820654bb3c20f2d6dd

View on Chainz ↗

Height

#327,283

Difficulty

10.176092

Transactions

Size

1.01 KB

Version

Bits

0a2d1457

Nonce

2,241

Timestamp

12/24/2013, 10:54:18 AM

Confirmations

6,482,519

Mined by

⛏️ saRgAe6gEbs5i5LrBXcGb93Lduqktkm5Mn8oYw

Merkle Root

9fcc0c3475c52fdf4524abab0f51d0d16949feb0b985431573b92dffc037e1de

Transactions (1)

Coinbase9fcc0c3475c52f…b92dffc037e1de

1 in → 26 out9.6400 XPM947 B

Ae6gEbs5…m5Mn8oYw AP5UvYhU…vLTDwkdA AG5YAjec…VhA4Aeh1 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR

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.

1.612 × 10⁹¹(92-digit number)

16123858744666083491…14481013872250353709

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

1.612 × 10⁹¹(92-digit number)

16123858744666083491…14481013872250353709

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.612 × 10⁹¹(92-digit number)

16123858744666083491…14481013872250353711

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

3.224 × 10⁹¹(92-digit number)

32247717489332166982…28962027744500707419

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.224 × 10⁹¹(92-digit number)

32247717489332166982…28962027744500707421

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

6.449 × 10⁹¹(92-digit number)

64495434978664333964…57924055489001414839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.449 × 10⁹¹(92-digit number)

64495434978664333964…57924055489001414841

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

1.289 × 10⁹²(93-digit number)

12899086995732866792…15848110978002829679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.289 × 10⁹²(93-digit number)

12899086995732866792…15848110978002829681

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

2.579 × 10⁹²(93-digit number)

25798173991465733585…31696221956005659359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.579 × 10⁹²(93-digit number)

25798173991465733585…31696221956005659361

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 #327,283

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