Block #504,646

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/21/2014, 9:55:19 PM · Difficulty 10.8102 · 6,306,123 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

360b1ec7a60ea531f0c0b67563302c0370850a8ca041c196703397aa74da756b

View on Chainz ↗

Height

#504,646

Difficulty

10.810215

Transactions

Size

766 B

Version

Bits

0acf6a38

Nonce

23,892,481

Timestamp

4/21/2014, 9:55:19 PM

Confirmations

6,306,123

Mined by

⛏️ FaSU:AREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

16ff70bea21900dc7eab0444c45debae1cdc8bc1907568f0b69fb6c4eedab42b

Transactions (1)

Coinbase16ff70bea21900…9fb6c4eedab42b

1 in → 18 out8.5400 XPM675 B

AREQGaCC…V47D9Shh ATKK7iFz…wZm46KN1 AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 AJzWx2VD…j4ZSMit5

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.

3.693 × 10⁹⁷(98-digit number)

36933377497871477869…04499848191539653079

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

3.693 × 10⁹⁷(98-digit number)

36933377497871477869…04499848191539653079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.693 × 10⁹⁷(98-digit number)

36933377497871477869…04499848191539653081

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

7.386 × 10⁹⁷(98-digit number)

73866754995742955738…08999696383079306159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.386 × 10⁹⁷(98-digit number)

73866754995742955738…08999696383079306161

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

1.477 × 10⁹⁸(99-digit number)

14773350999148591147…17999392766158612319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.477 × 10⁹⁸(99-digit number)

14773350999148591147…17999392766158612321

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

2.954 × 10⁹⁸(99-digit number)

29546701998297182295…35998785532317224639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.954 × 10⁹⁸(99-digit number)

29546701998297182295…35998785532317224641

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

5.909 × 10⁹⁸(99-digit number)

59093403996594364591…71997571064634449279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.909 × 10⁹⁸(99-digit number)

59093403996594364591…71997571064634449281

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 #504,646

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