Block #412,841

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/20/2014, 7:11:31 PM · Difficulty 10.4205 · 6,385,283 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53802e3a8dafaba555fe7525ad5547eadfffa6de6f2f4538928892ec427e6073

View on Chainz ↗

Height

#412,841

Difficulty

10.420544

Transactions

Size

1.58 KB

Version

Bits

0a6ba8c6

Nonce

50,056

Timestamp

2/20/2014, 7:11:31 PM

Confirmations

6,385,283

Mined by

⛏️ LaSS>AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

10201f5858bb1bd9ee0d221cd265c5fdf6c181e37652cdea380a0f80adb93932

Transactions (4)

Coinbase7a1e7b46798949…04b71204ab8459

1 in → 23 out9.1900 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

71cdbe6b1c5195…5ea4c7ed2e1bf5

1 in → 2 out7.3477 XPM227 B

APGF6ui3…J7QcQtin AeZZPYHj…5K1XcjZJ

3298474d5e9b18…b1080e683a0b0b

1 in → 2 out7.1499 XPM225 B

Ac5Zs4YY…USMWm5xJ AQBt5Am7…HMyQDePe

1d1222beead4b5…0ecb85baf2b70b

1 in → 2 out4.2645 XPM225 B

AGQ28qmE…jM1fPRww APjgy8Mm…kC5BpgKE

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.

4.486 × 10⁹⁸(99-digit number)

44861506741683270464…74531915789300844919

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

4.486 × 10⁹⁸(99-digit number)

44861506741683270464…74531915789300844919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.486 × 10⁹⁸(99-digit number)

44861506741683270464…74531915789300844921

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

8.972 × 10⁹⁸(99-digit number)

89723013483366540929…49063831578601689839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.972 × 10⁹⁸(99-digit number)

89723013483366540929…49063831578601689841

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

1.794 × 10⁹⁹(100-digit number)

17944602696673308185…98127663157203379679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.794 × 10⁹⁹(100-digit number)

17944602696673308185…98127663157203379681

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

3.588 × 10⁹⁹(100-digit number)

35889205393346616371…96255326314406759359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.588 × 10⁹⁹(100-digit number)

35889205393346616371…96255326314406759361

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

7.177 × 10⁹⁹(100-digit number)

71778410786693232743…92510652628813518719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.177 × 10⁹⁹(100-digit number)

71778410786693232743…92510652628813518721

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