Block #177,238

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/23/2013, 12:50:02 PM · Difficulty 9.8647 · 6,632,388 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c2d5fa787f6cf9e73fadf2ea873325c55b64930072d1214a04a58b8d24da9d8

View on Chainz ↗

Height

#177,238

Difficulty

9.864651

Transactions

Size

358 B

Version

Bits

09dd59c8

Nonce

74,626

Timestamp

9/23/2013, 12:50:02 PM

Confirmations

6,632,388

Mined by

⛏️ P2SHAXCPX9nvgBLLU11XbGCUxFqRGsbLwn58vJ

Merkle Root

e1ed8f1098451fbd021b47b30cab605e176fdf90b319f2b8fcd018fcc11971f9

Transactions (2)

Coinbase14fc08ef9b0e2d…6fab7771789902

1 in → 1 out10.2700 XPM109 B

AXCPX9nv…bLwn58vJ

743648985dfb0f…cfcef39395d611

1 in → 1 out10.2600 XPM157 B

AZjAawhu…JwrCuhga

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.

4.784 × 10¹⁰⁰(101-digit number)

47841161785115446489…62854083712928486399

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

4.784 × 10¹⁰⁰(101-digit number)

47841161785115446489…62854083712928486399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.784 × 10¹⁰⁰(101-digit number)

47841161785115446489…62854083712928486401

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

9.568 × 10¹⁰⁰(101-digit number)

95682323570230892979…25708167425856972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.568 × 10¹⁰⁰(101-digit number)

95682323570230892979…25708167425856972801

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

1.913 × 10¹⁰¹(102-digit number)

19136464714046178595…51416334851713945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.913 × 10¹⁰¹(102-digit number)

19136464714046178595…51416334851713945601

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

3.827 × 10¹⁰¹(102-digit number)

38272929428092357191…02832669703427891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.827 × 10¹⁰¹(102-digit number)

38272929428092357191…02832669703427891201

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

7.654 × 10¹⁰¹(102-digit number)

76545858856184714383…05665339406855782399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #177,238

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