Block #541,606

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/13/2014, 2:16:55 PM · Difficulty 10.9401 · 6,267,772 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a393585bea6fed82ea77a91cc5b308ff163ba02e6c1e238ea42368867aa831fa

View on Chainz ↗

Height

#541,606

Difficulty

10.940106

Transactions

Size

1.25 KB

Version

Bits

0af0aac9

Nonce

139,909,235

Timestamp

5/13/2014, 2:16:55 PM

Confirmations

6,267,772

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

81605a712f91c2ef7c6e04cc53d2f414f5efcb25ecbf1202770ad7fe83e09f81

Transactions (3)

Coinbase335ed37e70a7b2…c8146ae72b15d7

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

105dacd861598a…f32f1417015295

4 in → 2 out66.9114 XPM672 B

AUqwyMpF…6ugJsrSM AeKNgJMN…yKzdV3iJ

6a34b57ea43245…e6d49a47ba953a

1 in → 7 out8.3600 XPM396 B

AX5T243E…VQBn2F4b ALK6suqY…4jrUq48Q AR25VzqZ…XoYrxwMw AeJ2KovV…kXAjjLqC ATrEQ54T…JxtLzxQg

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.

2.005 × 10¹⁰⁰(101-digit number)

20052473877114474291…97030832945945861119

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

2.005 × 10¹⁰⁰(101-digit number)

20052473877114474291…97030832945945861119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.005 × 10¹⁰⁰(101-digit number)

20052473877114474291…97030832945945861121

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

4.010 × 10¹⁰⁰(101-digit number)

40104947754228948583…94061665891891722239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.010 × 10¹⁰⁰(101-digit number)

40104947754228948583…94061665891891722241

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

8.020 × 10¹⁰⁰(101-digit number)

80209895508457897167…88123331783783444479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.020 × 10¹⁰⁰(101-digit number)

80209895508457897167…88123331783783444481

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

1.604 × 10¹⁰¹(102-digit number)

16041979101691579433…76246663567566888959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.604 × 10¹⁰¹(102-digit number)

16041979101691579433…76246663567566888961

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

3.208 × 10¹⁰¹(102-digit number)

32083958203383158866…52493327135133777919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.208 × 10¹⁰¹(102-digit number)

32083958203383158866…52493327135133777921

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 #541,606

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