Block #477,215

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 8:11:04 AM · Difficulty 10.4785 · 6,326,706 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d36d09e32a36855f5be366cdfe85d59c641fa3ef30124b2a0c0d4c7db5f43fa

View on Chainz ↗

Height

#477,215

Difficulty

10.478515

Transactions

Size

661 B

Version

Bits

0a7a7ff7

Nonce

15,968

Timestamp

4/6/2014, 8:11:04 AM

Confirmations

6,326,706

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cead5703e97d9a8c63ebe22649bd932993e897fdefba84bc884fc750b7eb8ddb

Transactions (3)

Coinbase3d4f6a92f37267…e1841fe98b575a

1 in → 1 out9.1100 XPM116 B

AbwWkWZt…kawDhufa

b0d995a9622979…a479be5ead3883

1 in → 2 out6.0392 XPM226 B

AN2e32nF…QGpCRaAd AaY3TrYd…FpEg6ghH

d1933d3facf654…1222489d092233

1 in → 2 out2.5372 XPM227 B

AMEVtaAH…sTMnZQME AbkDKWUt…ik8Jwo7S

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.

2.609 × 10⁹⁹(100-digit number)

26096111103487730383…88398439746800703679

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

2.609 × 10⁹⁹(100-digit number)

26096111103487730383…88398439746800703679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.609 × 10⁹⁹(100-digit number)

26096111103487730383…88398439746800703681

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

5.219 × 10⁹⁹(100-digit number)

52192222206975460766…76796879493601407359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.219 × 10⁹⁹(100-digit number)

52192222206975460766…76796879493601407361

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

1.043 × 10¹⁰⁰(101-digit number)

10438444441395092153…53593758987202814719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.043 × 10¹⁰⁰(101-digit number)

10438444441395092153…53593758987202814721

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

2.087 × 10¹⁰⁰(101-digit number)

20876888882790184306…07187517974405629439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.087 × 10¹⁰⁰(101-digit number)

20876888882790184306…07187517974405629441

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

4.175 × 10¹⁰⁰(101-digit number)

41753777765580368612…14375035948811258879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.175 × 10¹⁰⁰(101-digit number)

41753777765580368612…14375035948811258881

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