Block #444,867

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 12:40:42 PM · Difficulty 10.3523 · 6,363,474 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4fba7b8d61bbcd49ff1b6a42f752e546692da20501f3db486ae3198f68989c1

View on Chainz ↗

Height

#444,867

Difficulty

10.352276

Transactions

Size

933 B

Version

Bits

0a5a2ec5

Nonce

22,441

Timestamp

3/15/2014, 12:40:42 PM

Confirmations

6,363,474

Mined by

⛏️ aS$JAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

20026657363aa273b893b6e888dee8af8433dbc855cf4204cff190a459febdd7

Transactions (1)

Coinbase20026657363aa2…f190a459febdd7

1 in → 23 out9.3200 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe Aac9Hjdg…P4ktypc3 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.

3.882 × 10⁹⁰(91-digit number)

38825514130775691768…66658609053430531689

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

3.882 × 10⁹⁰(91-digit number)

38825514130775691768…66658609053430531689

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.882 × 10⁹⁰(91-digit number)

38825514130775691768…66658609053430531691

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

7.765 × 10⁹⁰(91-digit number)

77651028261551383537…33317218106861063379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.765 × 10⁹⁰(91-digit number)

77651028261551383537…33317218106861063381

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

1.553 × 10⁹¹(92-digit number)

15530205652310276707…66634436213722126759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.553 × 10⁹¹(92-digit number)

15530205652310276707…66634436213722126761

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

3.106 × 10⁹¹(92-digit number)

31060411304620553415…33268872427444253519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.106 × 10⁹¹(92-digit number)

31060411304620553415…33268872427444253521

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

6.212 × 10⁹¹(92-digit number)

62120822609241106830…66537744854888507039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.212 × 10⁹¹(92-digit number)

62120822609241106830…66537744854888507041

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 #444,867

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