Block #545,023

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/15/2014, 4:12:22 AM · Difficulty 10.9524 · 6,272,414 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

717539da5da4f2b0bdb19e359db4fdbf404270de0479bd41838318337cdd5047

View on Chainz ↗

Height

#545,023

Difficulty

10.952351

Transactions

Size

1.30 KB

Version

Bits

0af3cd47

Nonce

441,983,166

Timestamp

5/15/2014, 4:12:22 AM

Confirmations

6,272,414

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

305368b4b2c10c9b2d468671ed0c94f2b20b769deda3bd315f5c3d82a67ad805

Transactions (4)

Coinbase39467bcf0ec222…99f27a4e8d5f40

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

3d95bd8756c799…bee1ef98c7fc58

2 in → 2 out10.6608 XPM373 B

AcFHn5wa…Zo6a5v3b AJjsAS7f…JwwbsDa7

52d868c10d3453…a3e9c584d95fb8

1 in → 2 out6.0154 XPM226 B

AKa2QsTL…naZxWo35 AWEm1NVx…BSyUpTdF

a96ce53d69fde5…1c77bf30623fc3

3 in → 2 out5.1661 XPM520 B

ASUbvGQ3…eWcvX9ZX AMik7k7o…kPuFQWga

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.

3.423 × 10⁹⁸(99-digit number)

34237542123513912443…85913676541003789439

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

3.423 × 10⁹⁸(99-digit number)

34237542123513912443…85913676541003789439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.423 × 10⁹⁸(99-digit number)

34237542123513912443…85913676541003789441

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

6.847 × 10⁹⁸(99-digit number)

68475084247027824886…71827353082007578879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.847 × 10⁹⁸(99-digit number)

68475084247027824886…71827353082007578881

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

1.369 × 10⁹⁹(100-digit number)

13695016849405564977…43654706164015157759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.369 × 10⁹⁹(100-digit number)

13695016849405564977…43654706164015157761

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

2.739 × 10⁹⁹(100-digit number)

27390033698811129954…87309412328030315519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.739 × 10⁹⁹(100-digit number)

27390033698811129954…87309412328030315521

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

5.478 × 10⁹⁹(100-digit number)

54780067397622259908…74618824656060631039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.478 × 10⁹⁹(100-digit number)

54780067397622259908…74618824656060631041

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

Block #545,023

Cookie Preferences