Block #482,278

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 10:01:51 AM · Difficulty 10.5418 · 6,326,767 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c3abf74178a245e1d093a627811d01640bb5eba6b9ba0fd573e952c74118a2b

View on Chainz ↗

Height

#482,278

Difficulty

10.541812

Transactions

Size

1.36 KB

Version

Bits

0a8ab432

Nonce

708,088

Timestamp

4/9/2014, 10:01:51 AM

Confirmations

6,326,767

Mined by

⛏️ TmAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

5d50f8864d4cbfdc5fd3c2501b4eadcf92af97b488d4bc9ce8540c8f82803200

Transactions (3)

Coinbase54c611be36e9a5…bba30581dd0120

1 in → 23 out9.0000 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AXCpMYgL…1r94ZQDa AZ34NcPy…8FPeFjPV ATp4jJhs…TbSgR8Qb

4fa37e94ab8601…2143e5e04d4a43

1 in → 2 out3.9682 XPM226 B

AJqnshVr…d3uKRLfd AJcs1wGu…PLmhe8Xa

f638ad0712f039…eaad16c0918f78

1 in → 2 out2.1438 XPM226 B

AXiNPjSx…ghhATApz Aaffr4EL…bJQCxKCY

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.

3.816 × 10⁹⁸(99-digit number)

38163320610058016905…12984694258684078399

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

3.816 × 10⁹⁸(99-digit number)

38163320610058016905…12984694258684078399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.816 × 10⁹⁸(99-digit number)

38163320610058016905…12984694258684078401

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

7.632 × 10⁹⁸(99-digit number)

76326641220116033811…25969388517368156799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.632 × 10⁹⁸(99-digit number)

76326641220116033811…25969388517368156801

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

1.526 × 10⁹⁹(100-digit number)

15265328244023206762…51938777034736313599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.526 × 10⁹⁹(100-digit number)

15265328244023206762…51938777034736313601

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

3.053 × 10⁹⁹(100-digit number)

30530656488046413524…03877554069472627199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.053 × 10⁹⁹(100-digit number)

30530656488046413524…03877554069472627201

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

6.106 × 10⁹⁹(100-digit number)

61061312976092827049…07755108138945254399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.106 × 10⁹⁹(100-digit number)

61061312976092827049…07755108138945254401

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 #482,278

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