Block #445,929

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 5:28:44 AM · Difficulty 10.3592 · 6,380,250 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8bbcbfdf2ad5eb44626e3ba01c2c5464cae427147ad27ed608572641a7726605

View on Chainz ↗

Height

#445,929

Difficulty

10.359158

Transactions

Size

937 B

Version

Bits

0a5bf1cc

Nonce

19,695

Timestamp

3/16/2014, 5:28:44 AM

Confirmations

6,380,250

Mined by

⛏️ aS%6n>AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b1a032930e01ab5628488bcc7b370a3a8fa272b43b6ee861feb32e96b2855016

Transactions (1)

Coinbaseb1a032930e01ab…b32e96b2855016

1 in → 23 out9.3000 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe AGKhfQo2…h7fBXLX6 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.

5.913 × 10⁹⁸(99-digit number)

59136247401935966658…91676397644420102999

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

5.913 × 10⁹⁸(99-digit number)

59136247401935966658…91676397644420102999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.913 × 10⁹⁸(99-digit number)

59136247401935966658…91676397644420103001

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

1.182 × 10⁹⁹(100-digit number)

11827249480387193331…83352795288840205999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.182 × 10⁹⁹(100-digit number)

11827249480387193331…83352795288840206001

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

2.365 × 10⁹⁹(100-digit number)

23654498960774386663…66705590577680411999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.365 × 10⁹⁹(100-digit number)

23654498960774386663…66705590577680412001

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

4.730 × 10⁹⁹(100-digit number)

47308997921548773327…33411181155360823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.730 × 10⁹⁹(100-digit number)

47308997921548773327…33411181155360824001

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

9.461 × 10⁹⁹(100-digit number)

94617995843097546654…66822362310721647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.461 × 10⁹⁹(100-digit number)

94617995843097546654…66822362310721648001

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 #445,929

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