Block #431,248

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 2:27:01 AM · Difficulty 10.3376 · 6,375,018 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

27b889fc50328e916cdbaded3d1a7a56b27ba936074caaf9393130fea539b325

View on Chainz ↗

Height

#431,248

Difficulty

10.337589

Transactions

Size

1.58 KB

Version

Bits

0a566c42

Nonce

365

Timestamp

3/6/2014, 2:27:01 AM

Confirmations

6,375,018

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7bd38a3e68313922678d5a7c523ea25797578ecfc927e7d7a59a3e70592229f1

Transactions (4)

Coinbase0c063e1c6290ee…c290bb5f7b4126

1 in → 1 out9.3700 XPM116 B

AbwWkWZt…kawDhufa

de4380310e0e76…d6f6a6b41f60ad

4 in → 11 out37.3400 XPM840 B

Ac7njVur…DfY6Hpwr AcQ4kegj…i4yJj88D AQpsy9pD…aHseMfku APiJPPBV…oMd88xJd AdKrkQzd…yvN4n1W8

bd8e7d24de960b…8af2300b1bd159

2 in → 2 out10.4032 XPM374 B

AMo4xYNR…6LV3Le7K AUXnj6vT…9CBLLryc

02a6b4db574b86…42ea7152be3dd6

1 in → 1 out1.9901 XPM191 B

ATx67UDN…RMYzJGRy

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.

4.202 × 10¹⁰⁰(101-digit number)

42029014310589125259…39992957344200785919

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

4.202 × 10¹⁰⁰(101-digit number)

42029014310589125259…39992957344200785919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.202 × 10¹⁰⁰(101-digit number)

42029014310589125259…39992957344200785921

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

8.405 × 10¹⁰⁰(101-digit number)

84058028621178250518…79985914688401571839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.405 × 10¹⁰⁰(101-digit number)

84058028621178250518…79985914688401571841

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

1.681 × 10¹⁰¹(102-digit number)

16811605724235650103…59971829376803143679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.681 × 10¹⁰¹(102-digit number)

16811605724235650103…59971829376803143681

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

3.362 × 10¹⁰¹(102-digit number)

33623211448471300207…19943658753606287359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.362 × 10¹⁰¹(102-digit number)

33623211448471300207…19943658753606287361

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

6.724 × 10¹⁰¹(102-digit number)

67246422896942600414…39887317507212574719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.724 × 10¹⁰¹(102-digit number)

67246422896942600414…39887317507212574721

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 #431,248

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