Block #448,005

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 3:07:18 PM · Difficulty 10.3675 · 6,350,834 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75a1212c28e135052d83792a860f09b1954ae229a9e4b40b4164fd26657d3d72

View on Chainz ↗

Height

#448,005

Difficulty

10.367483

Transactions

Size

1.50 KB

Version

Bits

0a5e1363

Nonce

56,632

Timestamp

3/17/2014, 3:07:18 PM

Confirmations

6,350,834

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

68f767d74367da293fb0d2b582ad5c9a087d588aa218e157db3aba37d462009b

Transactions (4)

Coinbase9eff1012e75329…4b7c2b3f2731ea

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

e529f5b01b0ea8…eac23e65a13646

4 in → 12 out37.3800 XPM877 B

APQt6ytQ…cVEqnYvo AThucpHS…u81AqEsr AKRt6uwL…VYA8uNG3 AeKNrjNj…1NEq95Ta APkSf5C5…wYwrjSQa

920ddafc9b57e8…3cd8a75cab45b2

1 in → 2 out3.7077 XPM226 B

AU52Uga5…pN7Lu1sV AcbbYPLg…3vp3W2JU

6fc13920c8f9e1…fb9736242bfaaa

1 in → 2 out2.0178 XPM226 B

AWKCrLY5…TP9YccMG AH9HenSr…7F72AXru

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.

1.209 × 10¹⁰²(103-digit number)

12092492688482299003…99333464460278984959

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

1.209 × 10¹⁰²(103-digit number)

12092492688482299003…99333464460278984959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.209 × 10¹⁰²(103-digit number)

12092492688482299003…99333464460278984961

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

2.418 × 10¹⁰²(103-digit number)

24184985376964598007…98666928920557969919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.418 × 10¹⁰²(103-digit number)

24184985376964598007…98666928920557969921

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

4.836 × 10¹⁰²(103-digit number)

48369970753929196015…97333857841115939839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.836 × 10¹⁰²(103-digit number)

48369970753929196015…97333857841115939841

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

9.673 × 10¹⁰²(103-digit number)

96739941507858392030…94667715682231879679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.673 × 10¹⁰²(103-digit number)

96739941507858392030…94667715682231879681

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

1.934 × 10¹⁰³(104-digit number)

19347988301571678406…89335431364463759359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.934 × 10¹⁰³(104-digit number)

19347988301571678406…89335431364463759361

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