Block #437,576

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 9:48:19 AM · Difficulty 10.3577 · 6,380,398 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

140615687b2b0552b043fc64c5e8a75a87ccfbc042fc0646b927991d601b57a6

View on Chainz ↗

Height

#437,576

Difficulty

10.357711

Transactions

Size

867 B

Version

Bits

0a5b92f5

Nonce

16,286

Timestamp

3/10/2014, 9:48:19 AM

Confirmations

6,380,398

Mined by

⛏️ HaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

fb26cdf6b43b397dcd45c1e19329c553f117bd6e6d0935a3a32c220e18804f15

Transactions (1)

Coinbasefb26cdf6b43b39…2c220e18804f15

1 in → 21 out9.3091 XPM777 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.

5.689 × 10⁹⁴(95-digit number)

56893108651727974035…39044279185715148799

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

5.689 × 10⁹⁴(95-digit number)

56893108651727974035…39044279185715148799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.689 × 10⁹⁴(95-digit number)

56893108651727974035…39044279185715148801

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

1.137 × 10⁹⁵(96-digit number)

11378621730345594807…78088558371430297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.137 × 10⁹⁵(96-digit number)

11378621730345594807…78088558371430297601

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

2.275 × 10⁹⁵(96-digit number)

22757243460691189614…56177116742860595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.275 × 10⁹⁵(96-digit number)

22757243460691189614…56177116742860595201

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

4.551 × 10⁹⁵(96-digit number)

45514486921382379228…12354233485721190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.551 × 10⁹⁵(96-digit number)

45514486921382379228…12354233485721190401

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

9.102 × 10⁹⁵(96-digit number)

91028973842764758456…24708466971442380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.102 × 10⁹⁵(96-digit number)

91028973842764758456…24708466971442380801

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 #437,576

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