Block #543,519

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/14/2014, 10:37:23 AM · Difficulty 10.9479 · 6,256,013 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

35f5d172f73bfef3931430d879d3ac193fc1046b41aa8aff195aaf0e29f43b07

View on Chainz ↗

Height

#543,519

Difficulty

10.947852

Transactions

Size

17.33 KB

Version

Bits

0af2a673

Nonce

128,844,472

Timestamp

5/14/2014, 10:37:23 AM

Confirmations

6,256,013

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3cc7564733f36978bdcc9b9d5ac82ee7b27f70a5f08ff6142e4ed5e268a0b0a5

Transactions (2)

Coinbase9ba6e58a975482…ddb94584e5d4cf

1 in → 1 out8.5100 XPM116 B

ANSXnLY2…Sd25TjkD

a4683d7aa93a80…82a2654a1b4d6a

118 in → 2 out500.0152 XPM17.13 KB

AJjnK9uC…VreFquR4 AWEWMzDk…6o4Z6kav

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.

3.506 × 10¹⁰⁰(101-digit number)

35061861213267860964…48323126652308684799

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

3.506 × 10¹⁰⁰(101-digit number)

35061861213267860964…48323126652308684799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.506 × 10¹⁰⁰(101-digit number)

35061861213267860964…48323126652308684801

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

7.012 × 10¹⁰⁰(101-digit number)

70123722426535721929…96646253304617369599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.012 × 10¹⁰⁰(101-digit number)

70123722426535721929…96646253304617369601

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

1.402 × 10¹⁰¹(102-digit number)

14024744485307144385…93292506609234739199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.402 × 10¹⁰¹(102-digit number)

14024744485307144385…93292506609234739201

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

2.804 × 10¹⁰¹(102-digit number)

28049488970614288771…86585013218469478399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.804 × 10¹⁰¹(102-digit number)

28049488970614288771…86585013218469478401

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

5.609 × 10¹⁰¹(102-digit number)

56098977941228577543…73170026436938956799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.609 × 10¹⁰¹(102-digit number)

56098977941228577543…73170026436938956801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.121 × 10¹⁰²(103-digit number)

11219795588245715508…46340052873877913599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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