Block #407,822

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 5:57:11 AM · Difficulty 10.4292 · 6,402,739 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9911c4fa7e0dab6ce77e0fd6061c9a68396754c2e86b0c79a7c117585158a2b

View on Chainz ↗

Height

#407,822

Difficulty

10.429230

Transactions

Size

901 B

Version

Bits

0a6de203

Nonce

131,533

Timestamp

2/17/2014, 5:57:11 AM

Confirmations

6,402,739

Mined by

⛏️ 9aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1ea4c72a17208600344cc3f74123efaf61d6bbb9dfeab74a82393218566abeaf

Transactions (1)

Coinbase1ea4c72a172086…393218566abeaf

1 in → 22 out9.1800 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ANNg88pG…ppn21sTe AQwRN8bE…V8PsTcY9

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.

2.504 × 10⁹⁴(95-digit number)

25043013607664480112…30271924605237089759

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

2.504 × 10⁹⁴(95-digit number)

25043013607664480112…30271924605237089759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.504 × 10⁹⁴(95-digit number)

25043013607664480112…30271924605237089761

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

5.008 × 10⁹⁴(95-digit number)

50086027215328960224…60543849210474179519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.008 × 10⁹⁴(95-digit number)

50086027215328960224…60543849210474179521

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

1.001 × 10⁹⁵(96-digit number)

10017205443065792044…21087698420948359039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.001 × 10⁹⁵(96-digit number)

10017205443065792044…21087698420948359041

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

2.003 × 10⁹⁵(96-digit number)

20034410886131584089…42175396841896718079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.003 × 10⁹⁵(96-digit number)

20034410886131584089…42175396841896718081

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

4.006 × 10⁹⁵(96-digit number)

40068821772263168179…84350793683793436159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.006 × 10⁹⁵(96-digit number)

40068821772263168179…84350793683793436161

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 #407,822

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