Block #441,622

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 6:47:19 AM · Difficulty 10.3483 · 6,365,579 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95ef7815113f3bfb177de9eeee19428fb0e05adef0e316550e4d0bf97e958826

View on Chainz ↗

Height

#441,622

Difficulty

10.348274

Transactions

Size

798 B

Version

Bits

0a592884

Nonce

58,781

Timestamp

3/13/2014, 6:47:19 AM

Confirmations

6,365,579

Mined by

⛏️ aS!TDAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f63e167ab6d473abca54980569b1ae256dd844ccb2e786bf4fa1f70c3fffd6dd

Transactions (1)

Coinbasef63e167ab6d473…a1f70c3fffd6dd

1 in → 19 out9.3200 XPM709 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

1.599 × 10⁹²(93-digit number)

15995038978560363178…37743653466753810879

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

1.599 × 10⁹²(93-digit number)

15995038978560363178…37743653466753810879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.599 × 10⁹²(93-digit number)

15995038978560363178…37743653466753810881

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

3.199 × 10⁹²(93-digit number)

31990077957120726356…75487306933507621759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.199 × 10⁹²(93-digit number)

31990077957120726356…75487306933507621761

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

6.398 × 10⁹²(93-digit number)

63980155914241452712…50974613867015243519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.398 × 10⁹²(93-digit number)

63980155914241452712…50974613867015243521

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

1.279 × 10⁹³(94-digit number)

12796031182848290542…01949227734030487039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.279 × 10⁹³(94-digit number)

12796031182848290542…01949227734030487041

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

2.559 × 10⁹³(94-digit number)

25592062365696581085…03898455468060974079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.559 × 10⁹³(94-digit number)

25592062365696581085…03898455468060974081

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 #441,622

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