Block #437,655

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 11:01:23 AM · Difficulty 10.3584 · 6,376,343 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d92623332ccdd7ad9bfbbf177a02a38a02095a06edea8e6ded18bad6bea6799e

View on Chainz ↗

Height

#437,655

Difficulty

10.358410

Transactions

Size

901 B

Version

Bits

0a5bc0c6

Nonce

123,826

Timestamp

3/10/2014, 11:01:23 AM

Confirmations

6,376,343

Mined by

⛏️ aSkAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7ec8082f973d3256c17978e886dcb9e17232c541e7f8f11284d2306473a9cb1d

Transactions (1)

Coinbase7ec8082f973d32…d2306473a9cb1d

1 in → 22 out9.3100 XPM811 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 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.

1.062 × 10⁹⁴(95-digit number)

10621133609098388451…20084757714444822119

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

1.062 × 10⁹⁴(95-digit number)

10621133609098388451…20084757714444822119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.062 × 10⁹⁴(95-digit number)

10621133609098388451…20084757714444822121

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

2.124 × 10⁹⁴(95-digit number)

21242267218196776902…40169515428889644239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.124 × 10⁹⁴(95-digit number)

21242267218196776902…40169515428889644241

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

4.248 × 10⁹⁴(95-digit number)

42484534436393553805…80339030857779288479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.248 × 10⁹⁴(95-digit number)

42484534436393553805…80339030857779288481

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

8.496 × 10⁹⁴(95-digit number)

84969068872787107611…60678061715558576959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.496 × 10⁹⁴(95-digit number)

84969068872787107611…60678061715558576961

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

1.699 × 10⁹⁵(96-digit number)

16993813774557421522…21356123431117153919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.699 × 10⁹⁵(96-digit number)

16993813774557421522…21356123431117153921

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 #437,655

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