Block #543,819

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2014, 2:23:44 PM · Difficulty 10.9486 · 6,264,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2db230e494ec18634d89e5965e4f311688658fb3e12cf9ce22e3acf27bfee3ec

View on Chainz ↗

Height

#543,819

Difficulty

10.948620

Transactions

Size

865 B

Version

Bits

0af2d8c9

Nonce

1,191,358,269

Timestamp

5/14/2014, 2:23:44 PM

Confirmations

6,264,362

Mined by

⛏️ P2SHANyuE9cj9WVqjQkLiB1S6PHyk2vGeZyFu4

Merkle Root

359ed8dbb8e1e3976e52c683fb52546b7997c3c5dd511cbd36025ef31ccb13ba

Transactions (2)

Coinbase099e3e4e7a7206…c06eec79a39020

1 in → 1 out8.3400 XPM109 B

ANyuE9cj…vGeZyFu4

6b1e6c6536440d…79fc5374e24549

4 in → 2 out10.2183 XPM667 B

APKpNcJY…mvfeSbZ6 ASrCnREh…ueFjRQ5d

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.

9.882 × 10⁹⁰(91-digit number)

98825324661386358511…99340622913183464899

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

9.882 × 10⁹⁰(91-digit number)

98825324661386358511…99340622913183464899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.882 × 10⁹⁰(91-digit number)

98825324661386358511…99340622913183464901

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

1.976 × 10⁹¹(92-digit number)

19765064932277271702…98681245826366929799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.976 × 10⁹¹(92-digit number)

19765064932277271702…98681245826366929801

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

3.953 × 10⁹¹(92-digit number)

39530129864554543404…97362491652733859599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.953 × 10⁹¹(92-digit number)

39530129864554543404…97362491652733859601

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

7.906 × 10⁹¹(92-digit number)

79060259729109086809…94724983305467719199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.906 × 10⁹¹(92-digit number)

79060259729109086809…94724983305467719201

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

1.581 × 10⁹²(93-digit number)

15812051945821817361…89449966610935438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.581 × 10⁹²(93-digit number)

15812051945821817361…89449966610935438401

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 #543,819

Cookie Preferences