Block #491,004

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 5:39:15 AM · Difficulty 10.6799 · 6,316,133 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9bfcb7108cfcb8043e3943fa46651ae796df33897750d67752dabff3eae8343d

View on Chainz ↗

Height

#491,004

Difficulty

10.679934

Transactions

Size

934 B

Version

Bits

0aae1027

Nonce

11,330

Timestamp

4/14/2014, 5:39:15 AM

Confirmations

6,316,133

Mined by

⛏️ }aSKtAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f0cca177e5142b528ee594fc457484271e406281cb12eebbcdf2a5593e6da246

Transactions (1)

Coinbasef0cca177e5142b…f2a5593e6da246

1 in → 23 out8.7500 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR ALqxX1WA…hsKjbnXn

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.

5.418 × 10⁹¹(92-digit number)

54183878101298923075…24447784475936778239

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

5.418 × 10⁹¹(92-digit number)

54183878101298923075…24447784475936778239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.418 × 10⁹¹(92-digit number)

54183878101298923075…24447784475936778241

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

1.083 × 10⁹²(93-digit number)

10836775620259784615…48895568951873556479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.083 × 10⁹²(93-digit number)

10836775620259784615…48895568951873556481

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

2.167 × 10⁹²(93-digit number)

21673551240519569230…97791137903747112959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.167 × 10⁹²(93-digit number)

21673551240519569230…97791137903747112961

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

4.334 × 10⁹²(93-digit number)

43347102481039138460…95582275807494225919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.334 × 10⁹²(93-digit number)

43347102481039138460…95582275807494225921

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

8.669 × 10⁹²(93-digit number)

86694204962078276920…91164551614988451839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.669 × 10⁹²(93-digit number)

86694204962078276920…91164551614988451841

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 #491,004

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