Block #481,579

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 11:48:03 PM · Difficulty 10.5340 · 6,328,660 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4c61a2cf27cc11cf58e861549a8352ba4c0409c4890e433060bf20382a0c3f9

View on Chainz ↗

Height

#481,579

Difficulty

10.534017

Transactions

Size

2.21 KB

Version

Bits

0a88b55b

Nonce

86,829

Timestamp

4/8/2014, 11:48:03 PM

Confirmations

6,328,660

Mined by

⛏️ +YaSDAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d445483496296c19a8d46065c60a6e89f3a891050fde0addaf59d4e7b1bb70a3

Transactions (4)

Coinbase1aead525508e51…356087b99481a7

1 in → 22 out9.0000 XPM811 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1

df09ef73a34a7a…747b8ad49ede76

7 in → 2 out114.6700 XPM910 B

AJueWVoE…BohhQsYP AUXCdpkc…SgHbpWTJ

1b46dc1da57b97…dff36e36113d63

1 in → 2 out6.5236 XPM226 B

ASyR8kNF…mC1cXuXw AZdV5WCw…KuN9geW7

d2f3ced69e8cdd…878950303990f0

1 in → 2 out2.5189 XPM225 B

AM46r3HK…vu3NeXNe AbkFb3wH…bdfcDGtR

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.

1.131 × 10⁹⁸(99-digit number)

11313601421121291875…79125734899058264319

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

1.131 × 10⁹⁸(99-digit number)

11313601421121291875…79125734899058264319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.131 × 10⁹⁸(99-digit number)

11313601421121291875…79125734899058264321

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

2.262 × 10⁹⁸(99-digit number)

22627202842242583751…58251469798116528639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.262 × 10⁹⁸(99-digit number)

22627202842242583751…58251469798116528641

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

4.525 × 10⁹⁸(99-digit number)

45254405684485167502…16502939596233057279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.525 × 10⁹⁸(99-digit number)

45254405684485167502…16502939596233057281

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

9.050 × 10⁹⁸(99-digit number)

90508811368970335005…33005879192466114559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.050 × 10⁹⁸(99-digit number)

90508811368970335005…33005879192466114561

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

1.810 × 10⁹⁹(100-digit number)

18101762273794067001…66011758384932229119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.810 × 10⁹⁹(100-digit number)

18101762273794067001…66011758384932229121

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 #481,579

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