Block #441,625

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 6:49:52 AM · Difficulty 10.3484 · 6,355,266 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a5825a3744fa928049308c88d21c7426596781f0b992496da746c438f1d93a7

View on Chainz ↗

Height

#441,625

Difficulty

10.348425

Transactions

Size

1.14 KB

Version

Bits

0a593268

Nonce

199,152

Timestamp

3/13/2014, 6:49:52 AM

Confirmations

6,355,266

Mined by

⛏️ P2SHAbGAfHjS9P89GGo7BFweZMrisTs3iiQVQx

Merkle Root

c7b9ffb3cdf198cc4aa78c88d379caf759fce3044693ab9341f22c44a7e77934

Transactions (2)

Coinbase68a34d8cf06d0d…1e1112fb31d6df

1 in → 1 out9.3300 XPM109 B

AbGAfHjS…s3iiQVQx

e40c96f31a7181…6c50c880451127

6 in → 2 out3.4933 XPM965 B

AXYhD1MA…fQ1carYo APoxytXQ…SCbb96Uh

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.

2.600 × 10⁹⁹(100-digit number)

26004609833960995753…01627216240236785119

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

2.600 × 10⁹⁹(100-digit number)

26004609833960995753…01627216240236785119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.600 × 10⁹⁹(100-digit number)

26004609833960995753…01627216240236785121

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

5.200 × 10⁹⁹(100-digit number)

52009219667921991507…03254432480473570239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.200 × 10⁹⁹(100-digit number)

52009219667921991507…03254432480473570241

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

1.040 × 10¹⁰⁰(101-digit number)

10401843933584398301…06508864960947140479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.040 × 10¹⁰⁰(101-digit number)

10401843933584398301…06508864960947140481

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

2.080 × 10¹⁰⁰(101-digit number)

20803687867168796603…13017729921894280959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.080 × 10¹⁰⁰(101-digit number)

20803687867168796603…13017729921894280961

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

4.160 × 10¹⁰⁰(101-digit number)

41607375734337593206…26035459843788561919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.160 × 10¹⁰⁰(101-digit number)

41607375734337593206…26035459843788561921

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