Block #481,407

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 9:16:47 PM · Difficulty 10.5311 · 6,324,903 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2120348ab20ca80fd7476ffd7627da58331b77ac2f1213756d4c1d9f8fcf1633

View on Chainz ↗

Height

#481,407

Difficulty

10.531106

Transactions

Size

934 B

Version

Bits

0a87f68f

Nonce

73,926

Timestamp

4/8/2014, 9:16:47 PM

Confirmations

6,324,903

Mined by

⛏️ XaSDgAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

af3509f3a24f536e9534097853974fe1458e4962aca0ca52da114346b0f384f1

Transactions (1)

Coinbaseaf3509f3a24f53…114346b0f384f1

1 in → 23 out9.0000 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3

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.

1.432 × 10⁹³(94-digit number)

14324220309494766582…28930546843388017519

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

1.432 × 10⁹³(94-digit number)

14324220309494766582…28930546843388017519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.432 × 10⁹³(94-digit number)

14324220309494766582…28930546843388017521

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

2.864 × 10⁹³(94-digit number)

28648440618989533165…57861093686776035039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.864 × 10⁹³(94-digit number)

28648440618989533165…57861093686776035041

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

5.729 × 10⁹³(94-digit number)

57296881237979066330…15722187373552070079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.729 × 10⁹³(94-digit number)

57296881237979066330…15722187373552070081

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

1.145 × 10⁹⁴(95-digit number)

11459376247595813266…31444374747104140159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.145 × 10⁹⁴(95-digit number)

11459376247595813266…31444374747104140161

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

2.291 × 10⁹⁴(95-digit number)

22918752495191626532…62888749494208280319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.291 × 10⁹⁴(95-digit number)

22918752495191626532…62888749494208280321

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 #481,407

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