Block #452,520

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 3:33:12 PM · Difficulty 10.3905 · 6,360,335 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5a38805fc0c2ced32246b622abd6ce514a9c542efd66266ebfc5ee99f5b25b2e

View on Chainz ↗

Height

#452,520

Difficulty

10.390541

Transactions

Size

970 B

Version

Bits

0a63fa82

Nonce

77,919

Timestamp

3/20/2014, 3:33:12 PM

Confirmations

6,360,335

Mined by

⛏️ aS+AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

52d9d1721d050fef8ab5f52b854eb68b877e07625b3f265a11a7f532a7f836f7

Transactions (1)

Coinbase52d9d1721d050f…a7f532a7f836f7

1 in → 24 out9.2500 XPM879 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ ALqxX1WA…hsKjbnXn

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.

1.105 × 10⁹⁷(98-digit number)

11050968736578886358…62155627485823304479

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

1.105 × 10⁹⁷(98-digit number)

11050968736578886358…62155627485823304479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.105 × 10⁹⁷(98-digit number)

11050968736578886358…62155627485823304481

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

2.210 × 10⁹⁷(98-digit number)

22101937473157772717…24311254971646608959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.210 × 10⁹⁷(98-digit number)

22101937473157772717…24311254971646608961

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

4.420 × 10⁹⁷(98-digit number)

44203874946315545435…48622509943293217919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.420 × 10⁹⁷(98-digit number)

44203874946315545435…48622509943293217921

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

8.840 × 10⁹⁷(98-digit number)

88407749892631090870…97245019886586435839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.840 × 10⁹⁷(98-digit number)

88407749892631090870…97245019886586435841

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

1.768 × 10⁹⁸(99-digit number)

17681549978526218174…94490039773172871679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.768 × 10⁹⁸(99-digit number)

17681549978526218174…94490039773172871681

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 #452,520

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