Block #457,924

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 5:48:43 AM · Difficulty 10.4210 · 6,337,013 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3e52ab9c1f9fcc306efbf31f56edec08dcdf7e14ee7359f0a5389172eac8a32

View on Chainz ↗

Height

#457,924

Difficulty

10.420966

Transactions

Size

1000 B

Version

Bits

0a6bc46e

Nonce

17,998

Timestamp

3/24/2014, 5:48:43 AM

Confirmations

6,337,013

Mined by

⛏️ P2SHASXb8Msj7tnyLvWQxYzaaZ1YewBxGf64iZ

Merkle Root

e1d0d049e8ae778dbe7b4df9576b110708a551650f718dd3ab80f9903e0b0474

Transactions (2)

Coinbasebc87fbca53aa53…9846b59bc1fd03

1 in → 1 out9.2000 XPM102 B

ASXb8Msj…BxGf64iZ

ae8cbfc01cedd7…05303d69bd50de

4 in → 6 out12.0109 XPM807 B

AcJN5mhY…SR18Lsso AQhMzWVC…wfpJe2JS AdPYnVrm…VPr3HEKX ATfne49g…EMbPLKn4 ATEhsWeC…sqKLchSz

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.

4.528 × 10⁹⁶(97-digit number)

45288901423639127331…98303018181117341059

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

4.528 × 10⁹⁶(97-digit number)

45288901423639127331…98303018181117341059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.528 × 10⁹⁶(97-digit number)

45288901423639127331…98303018181117341061

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

9.057 × 10⁹⁶(97-digit number)

90577802847278254663…96606036362234682119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.057 × 10⁹⁶(97-digit number)

90577802847278254663…96606036362234682121

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

1.811 × 10⁹⁷(98-digit number)

18115560569455650932…93212072724469364239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.811 × 10⁹⁷(98-digit number)

18115560569455650932…93212072724469364241

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

3.623 × 10⁹⁷(98-digit number)

36231121138911301865…86424145448938728479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.623 × 10⁹⁷(98-digit number)

36231121138911301865…86424145448938728481

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

7.246 × 10⁹⁷(98-digit number)

72462242277822603730…72848290897877456959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.246 × 10⁹⁷(98-digit number)

72462242277822603730…72848290897877456961

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