Block #407,726

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 4:22:17 AM · Difficulty 10.4293 · 6,397,820 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

550ad35464e74325161945fe0cf9bdb3263c05e34defc4d6f242e15e7c7b47a7

View on Chainz ↗

Height

#407,726

Difficulty

10.429261

Transactions

Size

722 B

Version

Bits

0a6de40d

Nonce

379,864

Timestamp

2/17/2014, 4:22:17 AM

Confirmations

6,397,820

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

722458945c571811bee2db7d01ef9569037391bb4b575cd73df91ee5297e0f67

Transactions (2)

Coinbaseaa2e59a4981760…1e3f18a4057240

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

7d9e7d7b6b37d1…88f6c8e02f6922

3 in → 2 out3.6100 XPM520 B

AW1gEcRv…jin8eULe AU3LJJEp…ibQ3GKPu

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.

3.155 × 10⁹⁹(100-digit number)

31559233527809909094…56630492512284435199

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

3.155 × 10⁹⁹(100-digit number)

31559233527809909094…56630492512284435199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.155 × 10⁹⁹(100-digit number)

31559233527809909094…56630492512284435201

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

6.311 × 10⁹⁹(100-digit number)

63118467055619818189…13260985024568870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.311 × 10⁹⁹(100-digit number)

63118467055619818189…13260985024568870401

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

1.262 × 10¹⁰⁰(101-digit number)

12623693411123963637…26521970049137740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.262 × 10¹⁰⁰(101-digit number)

12623693411123963637…26521970049137740801

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

2.524 × 10¹⁰⁰(101-digit number)

25247386822247927275…53043940098275481599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.524 × 10¹⁰⁰(101-digit number)

25247386822247927275…53043940098275481601

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

5.049 × 10¹⁰⁰(101-digit number)

50494773644495854551…06087880196550963199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.049 × 10¹⁰⁰(101-digit number)

50494773644495854551…06087880196550963201

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