Block #475,441

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 5:59:08 AM · Difficulty 10.4564 · 6,322,710 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29b181a7b7cad5f3169768b1827f64eadc25668675da15557fdbf9836022ff04

View on Chainz ↗

Height

#475,441

Difficulty

10.456444

Transactions

Size

649 B

Version

Bits

0a74d984

Nonce

537,579,824

Timestamp

4/5/2014, 5:59:08 AM

Confirmations

6,322,710

Mined by

⛏️ P2SHAeMxo6phv56jJ2qf7pPAGj8UyqNkA49y2x

Merkle Root

de658f8861fafad6d6d6a65e6634c2ed91f8aeb61e4de5bd48c7e490b8a394f5

Transactions (3)

Coinbasebe80009af7e5de…f44b3f3a435173

1 in → 1 out9.1500 XPM109 B

AeMxo6ph…NkA49y2x

584b73d49740c4…f479dcc01e0834

1 in → 2 out6.0924 XPM225 B

AHDrf4Eg…LHmTVP7i AYXiQEyP…myu8sEHZ

194dbbfab1acc1…a52021b0129bec

1 in → 2 out2.0587 XPM226 B

AMaaPyei…o74FUo7o AXxp24rY…yi3yUFBu

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.

1.678 × 10⁹³(94-digit number)

16787342001243382273…67631923918162952069

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

1.678 × 10⁹³(94-digit number)

16787342001243382273…67631923918162952069

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.678 × 10⁹³(94-digit number)

16787342001243382273…67631923918162952071

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

3.357 × 10⁹³(94-digit number)

33574684002486764546…35263847836325904139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.357 × 10⁹³(94-digit number)

33574684002486764546…35263847836325904141

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

6.714 × 10⁹³(94-digit number)

67149368004973529092…70527695672651808279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.714 × 10⁹³(94-digit number)

67149368004973529092…70527695672651808281

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

1.342 × 10⁹⁴(95-digit number)

13429873600994705818…41055391345303616559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.342 × 10⁹⁴(95-digit number)

13429873600994705818…41055391345303616561

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

2.685 × 10⁹⁴(95-digit number)

26859747201989411636…82110782690607233119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.685 × 10⁹⁴(95-digit number)

26859747201989411636…82110782690607233121

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