Block #432,818

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/7/2014, 4:29:47 AM · Difficulty 10.3395 · 6,374,369 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4290d39e9e5542798865e0eaa076b86d4b2d7a6a14fc214ae032ac27f0d79f2

View on Chainz ↗

Height

#432,818

Difficulty

10.339495

Transactions

Size

1.01 KB

Version

Bits

0a56e92a

Nonce

168,773

Timestamp

3/7/2014, 4:29:47 AM

Confirmations

6,374,369

Mined by

⛏️ aSKAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

dad14e46b323ea1ec4bfee108521e8fd4a4d7cb9778a6972b69116945e60ddc3

Transactions (1)

Coinbasedad14e46b323ea…9116945e60ddc3

1 in → 26 out9.3400 XPM946 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx 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.

2.559 × 10⁹⁴(95-digit number)

25597464327690384884…14276484160353051039

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

2.559 × 10⁹⁴(95-digit number)

25597464327690384884…14276484160353051039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.559 × 10⁹⁴(95-digit number)

25597464327690384884…14276484160353051041

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

5.119 × 10⁹⁴(95-digit number)

51194928655380769768…28552968320706102079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.119 × 10⁹⁴(95-digit number)

51194928655380769768…28552968320706102081

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

1.023 × 10⁹⁵(96-digit number)

10238985731076153953…57105936641412204159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.023 × 10⁹⁵(96-digit number)

10238985731076153953…57105936641412204161

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

2.047 × 10⁹⁵(96-digit number)

20477971462152307907…14211873282824408319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.047 × 10⁹⁵(96-digit number)

20477971462152307907…14211873282824408321

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

4.095 × 10⁹⁵(96-digit number)

40955942924304615815…28423746565648816639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.095 × 10⁹⁵(96-digit number)

40955942924304615815…28423746565648816641

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 #432,818

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