Block #544,334

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2014, 8:13:22 PM · Difficulty 10.9503 · 6,251,525 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

475abf78487f89c79446d51ee83a2cbfe451176c168c4f2645ad4c95a751d872

View on Chainz ↗

Height

#544,334

Difficulty

10.950294

Transactions

Size

1.58 KB

Version

Bits

0af34671

Nonce

53,718

Timestamp

5/14/2014, 8:13:22 PM

Confirmations

6,251,525

Mined by

⛏️ P2SHAXbpyooSXrgsDVAsu6AkhX5vgBbup7bQTH

Merkle Root

6c56b3e4567e7de74aac7585d1578b98ccdecee57c505c625858eb61334cf722

Transactions (4)

Coinbase856b3f513f931b…69d201ff61a288

1 in → 1 out8.3600 XPM109 B

AXbpyooS…bup7bQTH

549bad25bf0959…f30bf8894368c0

5 in → 2 out36.3980 XPM817 B

AVYSUn6n…gcdzE7B1 ASi5Za5p…QdE7LJdw

953dadc9182bcd…38724db3a9fdc9

2 in → 2 out13.1676 XPM374 B

AT5yhZx1…nFmWRSLW ATPt7vHE…dmxyFTX8

a2c69cafbf315b…7f8b0e903585a3

1 in → 2 out4.7607 XPM226 B

APubeFFq…bazrePxY AZRXmHaH…fPNYQcfx

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.

6.382 × 10⁹⁶(97-digit number)

63823097705553036305…43322925974947819519

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

6.382 × 10⁹⁶(97-digit number)

63823097705553036305…43322925974947819519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.382 × 10⁹⁶(97-digit number)

63823097705553036305…43322925974947819521

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

1.276 × 10⁹⁷(98-digit number)

12764619541110607261…86645851949895639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.276 × 10⁹⁷(98-digit number)

12764619541110607261…86645851949895639041

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

2.552 × 10⁹⁷(98-digit number)

25529239082221214522…73291703899791278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.552 × 10⁹⁷(98-digit number)

25529239082221214522…73291703899791278081

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

5.105 × 10⁹⁷(98-digit number)

51058478164442429044…46583407799582556159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.105 × 10⁹⁷(98-digit number)

51058478164442429044…46583407799582556161

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

1.021 × 10⁹⁸(99-digit number)

10211695632888485808…93166815599165112319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.021 × 10⁹⁸(99-digit number)

10211695632888485808…93166815599165112321

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