Block #463,454

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 3:35:30 AM · Difficulty 10.4143 · 6,354,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d82a350d91ad4987cb3051af9c50165ab3e6c5c0c49dd550b7e78c2d243dc58

View on Chainz ↗

Height

#463,454

Difficulty

10.414337

Transactions

Size

1.72 KB

Version

Bits

0a6a1200

Nonce

266,041

Timestamp

3/28/2014, 3:35:30 AM

Confirmations

6,354,550

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

950a99d732eb4473968a2af93a62338bf65722f90fd21c998a3afca814f7d00f

Transactions (2)

Coinbase6a7e0103fa2607…e8e33934b6d32e

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

fe8b8070c946cf…2f15962d1eaa79

10 in → 2 out30.6636 XPM1.52 KB

AKEt9LSx…jcML1C46 AGP3dxwf…YnCwQHjV

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.

1.107 × 10¹⁰⁰(101-digit number)

11079123465010008013…88023092433797810919

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

1.107 × 10¹⁰⁰(101-digit number)

11079123465010008013…88023092433797810919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.107 × 10¹⁰⁰(101-digit number)

11079123465010008013…88023092433797810921

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

2.215 × 10¹⁰⁰(101-digit number)

22158246930020016026…76046184867595621839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.215 × 10¹⁰⁰(101-digit number)

22158246930020016026…76046184867595621841

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

4.431 × 10¹⁰⁰(101-digit number)

44316493860040032052…52092369735191243679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.431 × 10¹⁰⁰(101-digit number)

44316493860040032052…52092369735191243681

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

8.863 × 10¹⁰⁰(101-digit number)

88632987720080064105…04184739470382487359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.863 × 10¹⁰⁰(101-digit number)

88632987720080064105…04184739470382487361

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

1.772 × 10¹⁰¹(102-digit number)

17726597544016012821…08369478940764974719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.772 × 10¹⁰¹(102-digit number)

17726597544016012821…08369478940764974721

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 #463,454

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