Block #452,227

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 10:51:39 AM · Difficulty 10.3892 · 6,353,048 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

97a5d956dd794ee10e9ef8138d534ad9e68c1139a5efea7ecf24e4d7e90029c6

View on Chainz ↗

Height

#452,227

Difficulty

10.389225

Transactions

Size

3.30 KB

Version

Bits

0a63a43d

Nonce

64,162

Timestamp

3/20/2014, 10:51:39 AM

Confirmations

6,353,048

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6fb42fea5560bff020fe9cfd0bc8ff7ea35a38d16c483ab3bc9bcfa1fe68f123

Transactions (2)

Coinbase6ea6fe4f0cee25…7a64ea3249acf3

1 in → 1 out9.2900 XPM116 B

AbwWkWZt…kawDhufa

b4907a6386848a…bc7639060cae61

11 in → 45 out102.2100 XPM3.09 KB

ARapidPq…BD8pNF5M AUkdqaxr…4jcbMUQ7 AR8WV4KS…SChNuf3B AJjhokhu…9Cjwps9g AeXEE9bU…K7M3huKw

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.

2.891 × 10⁹⁹(100-digit number)

28912449080042784906…58143271006792834559

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

2.891 × 10⁹⁹(100-digit number)

28912449080042784906…58143271006792834559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.891 × 10⁹⁹(100-digit number)

28912449080042784906…58143271006792834561

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

5.782 × 10⁹⁹(100-digit number)

57824898160085569813…16286542013585669119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.782 × 10⁹⁹(100-digit number)

57824898160085569813…16286542013585669121

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

1.156 × 10¹⁰⁰(101-digit number)

11564979632017113962…32573084027171338239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.156 × 10¹⁰⁰(101-digit number)

11564979632017113962…32573084027171338241

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

2.312 × 10¹⁰⁰(101-digit number)

23129959264034227925…65146168054342676479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.312 × 10¹⁰⁰(101-digit number)

23129959264034227925…65146168054342676481

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

4.625 × 10¹⁰⁰(101-digit number)

46259918528068455850…30292336108685352959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.625 × 10¹⁰⁰(101-digit number)

46259918528068455850…30292336108685352961

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