Block #464,561

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 8:56:45 PM · Difficulty 10.4225 · 6,344,187 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a71bfdc3c7ab5588c0cd66d2072c92958d882d0379430b87a88b3f4eb7478242

View on Chainz ↗

Height

#464,561

Difficulty

10.422531

Transactions

Size

1005 B

Version

Bits

0a6c2b05

Nonce

901,698

Timestamp

3/28/2014, 8:56:45 PM

Confirmations

6,344,187

Mined by

⛏️ aS5AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

fd27ac4b5ee24f12600ceb67e963f239358055797b1c6ec050a3110a79c05060

Transactions (1)

Coinbasefd27ac4b5ee24f…a3110a79c05060

1 in → 25 out9.1900 XPM913 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJtNW28X…Syb4Ph5j

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.

3.697 × 10⁹⁸(99-digit number)

36972464984376347224…92897944439516120959

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

3.697 × 10⁹⁸(99-digit number)

36972464984376347224…92897944439516120959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.697 × 10⁹⁸(99-digit number)

36972464984376347224…92897944439516120961

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

7.394 × 10⁹⁸(99-digit number)

73944929968752694448…85795888879032241919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.394 × 10⁹⁸(99-digit number)

73944929968752694448…85795888879032241921

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

1.478 × 10⁹⁹(100-digit number)

14788985993750538889…71591777758064483839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.478 × 10⁹⁹(100-digit number)

14788985993750538889…71591777758064483841

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

2.957 × 10⁹⁹(100-digit number)

29577971987501077779…43183555516128967679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.957 × 10⁹⁹(100-digit number)

29577971987501077779…43183555516128967681

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

5.915 × 10⁹⁹(100-digit number)

59155943975002155559…86367111032257935359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.915 × 10⁹⁹(100-digit number)

59155943975002155559…86367111032257935361

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 #464,561

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