Block #443,998

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/14/2014, 10:58:23 PM · Difficulty 10.3456 · 6,364,343 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2e4f0bb52c8d3ba8a997f79a454f85cfbf9bc449fd43fa4ae2a1394f93b3b3c

View on Chainz ↗

Height

#443,998

Difficulty

10.345556

Transactions

Size

969 B

Version

Bits

0a587656

Nonce

323,476

Timestamp

3/14/2014, 10:58:23 PM

Confirmations

6,364,343

Mined by

⛏️ ^aS#kwAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

676433bec89a4d273ccd7c9d31962fd5781c05af7584d8033f1186e492fa02f4

Transactions (1)

Coinbase676433bec89a4d…1186e492fa02f4

1 in → 24 out9.3300 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AUnkFe8H…fvenjA4X

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.

1.139 × 10⁹⁵(96-digit number)

11393905163989775417…87859960361188418559

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

1.139 × 10⁹⁵(96-digit number)

11393905163989775417…87859960361188418559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.139 × 10⁹⁵(96-digit number)

11393905163989775417…87859960361188418561

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

2.278 × 10⁹⁵(96-digit number)

22787810327979550835…75719920722376837119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.278 × 10⁹⁵(96-digit number)

22787810327979550835…75719920722376837121

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

4.557 × 10⁹⁵(96-digit number)

45575620655959101671…51439841444753674239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.557 × 10⁹⁵(96-digit number)

45575620655959101671…51439841444753674241

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

9.115 × 10⁹⁵(96-digit number)

91151241311918203343…02879682889507348479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.115 × 10⁹⁵(96-digit number)

91151241311918203343…02879682889507348481

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

1.823 × 10⁹⁶(97-digit number)

18230248262383640668…05759365779014696959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.823 × 10⁹⁶(97-digit number)

18230248262383640668…05759365779014696961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.646 × 10⁹⁶(97-digit number)

36460496524767281337…11518731558029393919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #443,998

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