Block #473,605

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 12:46:37 AM · Difficulty 10.4461 · 6,317,547 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a8e09fa6f2af07e1fdb474921f4037ad8d74d02bcdac84108b5791b56c68e3d

View on Chainz ↗

Height

#473,605

Difficulty

10.446067

Transactions

Size

610 B

Version

Bits

0a72317a

Nonce

2,724

Timestamp

4/4/2014, 12:46:37 AM

Confirmations

6,317,547

Merkle Root

b9d079073d756e07c53527836afb08083a37f42e98e31e94d3ae0f2e7c5d3162

Transactions (2)

Coinbasedcda47741159d0…920b7484a4eacf

1 in → 1 out9.1600 XPM110 B

AKAhjZVk…yhTVER9U

81b6e3295ac132…389f381bf1c70f

2 in → 4 out9.7356 XPM408 B

Aai7rmvE…JWhtS5Q5 AKc9Rmjx…Bir3N5mm AeKNrjNj…1NEq95Ta AXqCJxua…RZtym3F2

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.

6.806 × 10⁹⁹(100-digit number)

68061598102600845288…86864982251369625599

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

6.806 × 10⁹⁹(100-digit number)

68061598102600845288…86864982251369625599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.806 × 10⁹⁹(100-digit number)

68061598102600845288…86864982251369625601

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

1.361 × 10¹⁰⁰(101-digit number)

13612319620520169057…73729964502739251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.361 × 10¹⁰⁰(101-digit number)

13612319620520169057…73729964502739251201

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

2.722 × 10¹⁰⁰(101-digit number)

27224639241040338115…47459929005478502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.722 × 10¹⁰⁰(101-digit number)

27224639241040338115…47459929005478502401

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

5.444 × 10¹⁰⁰(101-digit number)

54449278482080676231…94919858010957004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.444 × 10¹⁰⁰(101-digit number)

54449278482080676231…94919858010957004801

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

1.088 × 10¹⁰¹(102-digit number)

10889855696416135246…89839716021914009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.088 × 10¹⁰¹(102-digit number)

10889855696416135246…89839716021914009601

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