Block #543,098

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/14/2014, 6:15:13 AM · Difficulty 10.9462 · 6,266,891 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

230899298864600b0e7823df82358b41b06672f4cfed3d21528c75c9b7c9bcaa

View on Chainz ↗

Height

#543,098

Difficulty

10.946167

Transactions

Size

887 B

Version

Bits

0af237f9

Nonce

134,378,038

Timestamp

5/14/2014, 6:15:13 AM

Confirmations

6,266,891

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2e052855f8b76de8a96f768032072318adc751627f4b305b16e82e4a77e938ff

Transactions (4)

Coinbase3ef9b9fb6651c2…9e8a388f105e36

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

dcb06e6825b8ab…3541e3820acee9

1 in → 2 out7.8216 XPM226 B

ASUbvGQ3…eWcvX9ZX APgCa6Mb…qiZCNnms

cb0b7943708263…0354d8bdc0f4e2

1 in → 2 out1.5869 XPM226 B

AKweJ6z4…fiQLQ8zk AehpAz1S…p3fiiUqb

ceb5177a02cea6…18ed068e688aa5

1 in → 2 out7.3395 XPM227 B

ATjfQS9R…Qnp4sSir AYsF26zP…7fyKGL6Z

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.

2.324 × 10⁹⁸(99-digit number)

23242723007238109606…65835618469599129199

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

2.324 × 10⁹⁸(99-digit number)

23242723007238109606…65835618469599129199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.324 × 10⁹⁸(99-digit number)

23242723007238109606…65835618469599129201

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

4.648 × 10⁹⁸(99-digit number)

46485446014476219213…31671236939198258399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.648 × 10⁹⁸(99-digit number)

46485446014476219213…31671236939198258401

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

9.297 × 10⁹⁸(99-digit number)

92970892028952438426…63342473878396516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.297 × 10⁹⁸(99-digit number)

92970892028952438426…63342473878396516801

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

1.859 × 10⁹⁹(100-digit number)

18594178405790487685…26684947756793033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.859 × 10⁹⁹(100-digit number)

18594178405790487685…26684947756793033601

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

3.718 × 10⁹⁹(100-digit number)

37188356811580975370…53369895513586067199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.718 × 10⁹⁹(100-digit number)

37188356811580975370…53369895513586067201

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

7.437 × 10⁹⁹(100-digit number)

74376713623161950740…06739791027172134399

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

Block #543,098

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