Block #469,656

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 9:25:57 AM · Difficulty 10.4276 · 6,355,194 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4fc1dda049de69a6c038954fb0d62cf270e77e991efa02c4f3653ba9035cfbbf

View on Chainz ↗

Height

#469,656

Difficulty

10.427554

Transactions

Size

1.01 KB

Version

Bits

0a6d7431

Nonce

285,375

Timestamp

4/1/2014, 9:25:57 AM

Confirmations

6,355,194

Mined by

⛏️ P2SHASXb8Msj7tnyLvWQxYzaaZ1YewBxGf64iZ

Merkle Root

a57934002477ceee47b021574f570586616664c95b44e01a3630b0d5bf79aeda

Transactions (3)

Coinbase596a7ecb96de8e…8e60a51e03f584

1 in → 1 out9.2000 XPM101 B

ASXb8Msj…BxGf64iZ

04ccda3194c085…cf856c41a85760

3 in → 7 out23.9299 XPM622 B

AeKNrjNj…1NEq95Ta AKAPvhfV…MZpnyCXR APn2wJAF…3buAhEQY AcADmAoe…8iNnoMzB AHCuz9P2…41tUcRdy

c8bca58f730d09…ec2ab26aba79e6

1 in → 2 out6181.9945 XPM226 B

AatHwFtm…iZa5FqbZ AY4H42CP…4bQ4ZA3H

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.

5.890 × 10⁹¹(92-digit number)

58908032502700423792…70222412995051198719

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

5.890 × 10⁹¹(92-digit number)

58908032502700423792…70222412995051198719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.890 × 10⁹¹(92-digit number)

58908032502700423792…70222412995051198721

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

1.178 × 10⁹²(93-digit number)

11781606500540084758…40444825990102397439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.178 × 10⁹²(93-digit number)

11781606500540084758…40444825990102397441

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

2.356 × 10⁹²(93-digit number)

23563213001080169517…80889651980204794879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.356 × 10⁹²(93-digit number)

23563213001080169517…80889651980204794881

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

4.712 × 10⁹²(93-digit number)

47126426002160339034…61779303960409589759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.712 × 10⁹²(93-digit number)

47126426002160339034…61779303960409589761

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

9.425 × 10⁹²(93-digit number)

94252852004320678068…23558607920819179519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.425 × 10⁹²(93-digit number)

94252852004320678068…23558607920819179521

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 #469,656

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