Block #474,087

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 8:42:32 AM · Difficulty 10.4475 · 6,320,223 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43997ee06a379a5d160df197dae7c42e86603934238991d9369e906eee1fb656

View on Chainz ↗

Height

#474,087

Difficulty

10.447511

Transactions

Size

935 B

Version

Bits

0a72900f

Nonce

86,709

Timestamp

4/4/2014, 8:42:32 AM

Confirmations

6,320,223

Merkle Root

7daa5980ddb318d2474fdc351504126ed682198d73d9e1fee94153cdc91ed073

Transactions (1)

Coinbase7daa5980ddb318…4153cdc91ed073

1 in → 23 out9.1500 XPM844 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1

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.

2.042 × 10⁹⁸(99-digit number)

20424477635355041267…87444892503348550859

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

2.042 × 10⁹⁸(99-digit number)

20424477635355041267…87444892503348550859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.042 × 10⁹⁸(99-digit number)

20424477635355041267…87444892503348550861

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

4.084 × 10⁹⁸(99-digit number)

40848955270710082535…74889785006697101719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.084 × 10⁹⁸(99-digit number)

40848955270710082535…74889785006697101721

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

8.169 × 10⁹⁸(99-digit number)

81697910541420165070…49779570013394203439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.169 × 10⁹⁸(99-digit number)

81697910541420165070…49779570013394203441

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

1.633 × 10⁹⁹(100-digit number)

16339582108284033014…99559140026788406879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.633 × 10⁹⁹(100-digit number)

16339582108284033014…99559140026788406881

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

3.267 × 10⁹⁹(100-digit number)

32679164216568066028…99118280053576813759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.267 × 10⁹⁹(100-digit number)

32679164216568066028…99118280053576813761

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