Block #470,769

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 3:58:00 AM · Difficulty 10.4284 · 6,337,353 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99d8a6e282f3233182fc66fd5be71dae6a55bb66078a7da48bc933c87038417d

View on Chainz ↗

Height

#470,769

Difficulty

10.428408

Transactions

Size

429 B

Version

Bits

0a6dac29

Nonce

299,308

Timestamp

4/2/2014, 3:58:00 AM

Confirmations

6,337,353

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9ab8b97aacaf2e3990a51a5b7b695c1b88582b57355468de897710191e95e37b

Transactions (2)

Coinbasee5b08310875870…268ba8b5b501a9

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

d9eed4386f77e0…4fa5b8994d5bd9

1 in → 2 out15.4874 XPM226 B

AHwvxqCN…7z7foF67 APKLauX2…VghFAUWf

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.

4.546 × 10¹⁰¹(102-digit number)

45465036088730455513…03901566519712355839

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

4.546 × 10¹⁰¹(102-digit number)

45465036088730455513…03901566519712355839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.546 × 10¹⁰¹(102-digit number)

45465036088730455513…03901566519712355841

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

9.093 × 10¹⁰¹(102-digit number)

90930072177460911027…07803133039424711679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.093 × 10¹⁰¹(102-digit number)

90930072177460911027…07803133039424711681

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

1.818 × 10¹⁰²(103-digit number)

18186014435492182205…15606266078849423359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.818 × 10¹⁰²(103-digit number)

18186014435492182205…15606266078849423361

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

3.637 × 10¹⁰²(103-digit number)

36372028870984364411…31212532157698846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.637 × 10¹⁰²(103-digit number)

36372028870984364411…31212532157698846721

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

7.274 × 10¹⁰²(103-digit number)

72744057741968728822…62425064315397693439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.274 × 10¹⁰²(103-digit number)

72744057741968728822…62425064315397693441

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 #470,769

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