Block #476,133

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 3:38:54 PM · Difficulty 10.4691 · 6,319,403 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0e275dd820e8d73599469f1d515306f9e24ae9a49400ac9b17766920fbc8f65a

View on Chainz ↗

Height

#476,133

Difficulty

10.469106

Transactions

Size

1.23 KB

Version

Bits

0a781759

Nonce

204,070

Timestamp

4/5/2014, 3:38:54 PM

Confirmations

6,319,403

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

da57372f4738fc894e25e19c07332a95960cb10e4190ea6095f34b87d57d6571

Transactions (2)

Coinbasee84f81ac82ef50…bb070580fa2d0f

1 in → 1 out9.1300 XPM110 B

AeKNrjNj…1NEq95Ta

c7f36f00e41042…927ec209693460

5 in → 14 out45.8800 XPM1.03 KB

ANi1iTLk…n7Ddidrs AVRoiQ58…CXfzRWrM AQ8rAY3V…anzVDEuW AL9UZuKj…g3Q3eciV AXDEZh15…FbrAPGkC

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.

5.422 × 10¹⁰²(103-digit number)

54224188817355648884…74069338660853775359

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

5.422 × 10¹⁰²(103-digit number)

54224188817355648884…74069338660853775359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.422 × 10¹⁰²(103-digit number)

54224188817355648884…74069338660853775361

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

1.084 × 10¹⁰³(104-digit number)

10844837763471129776…48138677321707550719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.084 × 10¹⁰³(104-digit number)

10844837763471129776…48138677321707550721

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

2.168 × 10¹⁰³(104-digit number)

21689675526942259553…96277354643415101439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.168 × 10¹⁰³(104-digit number)

21689675526942259553…96277354643415101441

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

4.337 × 10¹⁰³(104-digit number)

43379351053884519107…92554709286830202879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.337 × 10¹⁰³(104-digit number)

43379351053884519107…92554709286830202881

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

8.675 × 10¹⁰³(104-digit number)

86758702107769038215…85109418573660405759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.675 × 10¹⁰³(104-digit number)

86758702107769038215…85109418573660405761

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