Block #541,838

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/13/2014, 4:37:51 PM · Difficulty 10.9412 · 6,269,018 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ca356d25c72fee9423ce5a516b61c30945349d1e0c9cb1f9a7f4607cd504909

View on Chainz ↗

Height

#541,838

Difficulty

10.941199

Transactions

Size

885 B

Version

Bits

0af0f264

Nonce

295,240,320

Timestamp

5/13/2014, 4:37:51 PM

Confirmations

6,269,018

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1a6d7f3ca70599040ebd60fa13ddb6d020391c1d1910f5d6bfc95a1bea4922e4

Transactions (4)

Coinbaseda954433eebd9d…50d838033fcd09

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

5db10dfa02bca2…1436637ff279ed

1 in → 2 out8.3600 XPM226 B

Ad7xBNNj…rHvy77SN AYuXtsY9…7h3id98y

f4d889c2e27408…75aa40b1820392

1 in → 2 out7.8446 XPM225 B

AeVyD2NN…Q8TXJTy5 AKHvsgDo…CSPY9gUt

a09821618b6d46…511c0f6cc83774

1 in → 2 out7.3425 XPM225 B

APgb9N5X…nBqsDcqb AYSZNV67…TJx3g2un

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.

1.195 × 10¹⁰¹(102-digit number)

11957558187376168212…47329517546369597439

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

1.195 × 10¹⁰¹(102-digit number)

11957558187376168212…47329517546369597439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.195 × 10¹⁰¹(102-digit number)

11957558187376168212…47329517546369597441

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

2.391 × 10¹⁰¹(102-digit number)

23915116374752336425…94659035092739194879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.391 × 10¹⁰¹(102-digit number)

23915116374752336425…94659035092739194881

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

4.783 × 10¹⁰¹(102-digit number)

47830232749504672850…89318070185478389759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.783 × 10¹⁰¹(102-digit number)

47830232749504672850…89318070185478389761

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

9.566 × 10¹⁰¹(102-digit number)

95660465499009345701…78636140370956779519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.566 × 10¹⁰¹(102-digit number)

95660465499009345701…78636140370956779521

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

1.913 × 10¹⁰²(103-digit number)

19132093099801869140…57272280741913559039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.913 × 10¹⁰²(103-digit number)

19132093099801869140…57272280741913559041

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 #541,838

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