Block #406,835

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/16/2014, 1:03:06 PM · Difficulty 10.4319 · 6,420,265 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3db0e214d9c14d1fb3c8939f6dbed6d8f582b01e95b338b99f6cb3de0cb3bc7c

View on Chainz ↗

Height

#406,835

Difficulty

10.431919

Transactions

Size

914 B

Version

Bits

0a6e9245

Nonce

306,354

Timestamp

2/16/2014, 1:03:06 PM

Confirmations

6,420,265

Mined by

⛏️ P2SHAGhYgLoiHNPSGWufmNuM4zCKo1TYaWoJv5

Merkle Root

28974b3db943f2bda4b472d0878d681b54854cc9bc473040dd73241890b4a6b9

Transactions (3)

Coinbase07efeeedd2680d…6d2ce64a24b9c3

1 in → 1 out9.1900 XPM109 B

AGhYgLoi…TYaWoJv5

bd382f084fa800…122e059d5b827a

2 in → 2 out219.4700 XPM373 B

AJZQUhuk…vZ3DTDtm AQUC7Hue…LL2XMoNY

fc12ec6000a87b…549e74c79896e3

2 in → 1 out82.7800 XPM340 B

AQUC7Hue…LL2XMoNY

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.

5.473 × 10⁹⁸(99-digit number)

54738223106961670974…33115609569241215999

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

5.473 × 10⁹⁸(99-digit number)

54738223106961670974…33115609569241215999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.473 × 10⁹⁸(99-digit number)

54738223106961670974…33115609569241216001

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

1.094 × 10⁹⁹(100-digit number)

10947644621392334194…66231219138482431999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.094 × 10⁹⁹(100-digit number)

10947644621392334194…66231219138482432001

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

2.189 × 10⁹⁹(100-digit number)

21895289242784668389…32462438276964863999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.189 × 10⁹⁹(100-digit number)

21895289242784668389…32462438276964864001

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

4.379 × 10⁹⁹(100-digit number)

43790578485569336779…64924876553929727999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.379 × 10⁹⁹(100-digit number)

43790578485569336779…64924876553929728001

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

8.758 × 10⁹⁹(100-digit number)

87581156971138673559…29849753107859455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.758 × 10⁹⁹(100-digit number)

87581156971138673559…29849753107859456001

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 #406,835

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