Block #431,408

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 5:05:25 AM · Difficulty 10.3384 · 6,371,965 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36dbc0e3782863fbb1c08ee1b5fb6b1f66bba88ba1beb80f07d2215b2e76122c

View on Chainz ↗

Height

#431,408

Difficulty

10.338442

Transactions

Size

9.46 KB

Version

Bits

0a56a41d

Nonce

7,920

Timestamp

3/6/2014, 5:05:25 AM

Confirmations

6,371,965

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c207051db0dd9d2859c5a9f4e48abd7606b7ff1241f0f906aa3f0192739fece2

Transactions (3)

Coinbase282afca65054ca…e7f4755c9d1f5f

1 in → 1 out9.4400 XPM116 B

AbwWkWZt…kawDhufa

47db5a48e9838c…5044c37c17d242

3 in → 2 out32.8319 XPM523 B

AKC6WKzi…rdi2BkMR AMAkko2K…LodFuPET

1e2d16cbf651e7…6d310278f1b688

60 in → 2 out183.2543 XPM8.74 KB

Aaq5ydQe…MWD3ZPck AWN5RAcE…ZpoQGDeS

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.

1.122 × 10⁹⁹(100-digit number)

11222640265464280786…28908771396179119359

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

1.122 × 10⁹⁹(100-digit number)

11222640265464280786…28908771396179119359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.122 × 10⁹⁹(100-digit number)

11222640265464280786…28908771396179119361

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

2.244 × 10⁹⁹(100-digit number)

22445280530928561573…57817542792358238719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.244 × 10⁹⁹(100-digit number)

22445280530928561573…57817542792358238721

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

4.489 × 10⁹⁹(100-digit number)

44890561061857123146…15635085584716477439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.489 × 10⁹⁹(100-digit number)

44890561061857123146…15635085584716477441

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

8.978 × 10⁹⁹(100-digit number)

89781122123714246293…31270171169432954879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.978 × 10⁹⁹(100-digit number)

89781122123714246293…31270171169432954881

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

1.795 × 10¹⁰⁰(101-digit number)

17956224424742849258…62540342338865909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.795 × 10¹⁰⁰(101-digit number)

17956224424742849258…62540342338865909761

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