Block #472,422

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 6:52:17 AM · Difficulty 10.4335 · 6,336,524 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec9c2a9c14895248eaf9b100b0e4b04a2b4fa664804817b9fd305c2bc1d8c9ef

View on Chainz ↗

Height

#472,422

Difficulty

10.433495

Transactions

Size

661 B

Version

Bits

0a6ef97f

Nonce

5,634

Timestamp

4/3/2014, 6:52:17 AM

Confirmations

6,336,524

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9a0f2f3fe76e8c6128128cd12402172c74d99f85734b7cc50ab9d9b24ddc2f34

Transactions (3)

Coinbased8774e8f243b67…c86e33bfe2464e

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

1cf1d8eda98999…bb22530628988f

1 in → 2 out5.1166 XPM226 B

AY5e3NVX…eaDMkuYN AXbdaSxe…wddmyL8o

c87135bd283d54…8d88d5987369cb

1 in → 2 out1.5851 XPM226 B

AKi4fscb…46sbQkcL Aeuc3WSZ…ythjLmc9

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.

5.471 × 10¹⁰⁰(101-digit number)

54710503361376876685…37316217734377689599

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

5.471 × 10¹⁰⁰(101-digit number)

54710503361376876685…37316217734377689599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.471 × 10¹⁰⁰(101-digit number)

54710503361376876685…37316217734377689601

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

1.094 × 10¹⁰¹(102-digit number)

10942100672275375337…74632435468755379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.094 × 10¹⁰¹(102-digit number)

10942100672275375337…74632435468755379201

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

2.188 × 10¹⁰¹(102-digit number)

21884201344550750674…49264870937510758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.188 × 10¹⁰¹(102-digit number)

21884201344550750674…49264870937510758401

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

4.376 × 10¹⁰¹(102-digit number)

43768402689101501348…98529741875021516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.376 × 10¹⁰¹(102-digit number)

43768402689101501348…98529741875021516801

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

8.753 × 10¹⁰¹(102-digit number)

87536805378203002696…97059483750043033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.753 × 10¹⁰¹(102-digit number)

87536805378203002696…97059483750043033601

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 #472,422

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