Block #482,377

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 11:12:17 AM · Difficulty 10.5444 · 6,311,910 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dcd93b7860c846aa1acde34a923c19dc341b1e5f60ffb694261d8e5a3a63aafc

View on Chainz ↗

Height

#482,377

Difficulty

10.544376

Transactions

Size

582 B

Version

Bits

0a8b5c3f

Nonce

95,432

Timestamp

4/9/2014, 11:12:17 AM

Confirmations

6,311,910

Merkle Root

6648b05bfebd2c12cc4d64538e62deeec32948dd9dc360dc7ac7c7c2c1d128fe

Transactions (2)

Coinbase1f9b398e8c6aeb…3b4909b0118e93

1 in → 1 out8.9900 XPM116 B

AbwWkWZt…kawDhufa

64d6e4607e7ccf…0d418d33ef78e3

2 in → 2 out10.0262 XPM374 B

ANGQYrEF…UTyTuyeV ALfKeL39…UDyJy1kH

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.

1.203 × 10⁹⁹(100-digit number)

12034537442016514732…13361965855223252799

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

1.203 × 10⁹⁹(100-digit number)

12034537442016514732…13361965855223252799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.203 × 10⁹⁹(100-digit number)

12034537442016514732…13361965855223252801

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

2.406 × 10⁹⁹(100-digit number)

24069074884033029464…26723931710446505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.406 × 10⁹⁹(100-digit number)

24069074884033029464…26723931710446505601

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

4.813 × 10⁹⁹(100-digit number)

48138149768066058929…53447863420893011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.813 × 10⁹⁹(100-digit number)

48138149768066058929…53447863420893011201

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

9.627 × 10⁹⁹(100-digit number)

96276299536132117859…06895726841786022399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.627 × 10⁹⁹(100-digit number)

96276299536132117859…06895726841786022401

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

1.925 × 10¹⁰⁰(101-digit number)

19255259907226423571…13791453683572044799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.925 × 10¹⁰⁰(101-digit number)

19255259907226423571…13791453683572044801

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