Block #324,011

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2013, 1:02:56 AM · Difficulty 10.2075 · 6,479,752 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5443f08ad1a4c2bfa94bb22eca71422bfa931c059c0e2bdceeb688c044dd8b6

View on Chainz ↗

Height

#324,011

Difficulty

10.207502

Transactions

Size

210 B

Version

Bits

0a351ed7

Nonce

15,232

Timestamp

12/22/2013, 1:02:56 AM

Confirmations

6,479,752

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

72a16e2e33d0fed3a86e28b8599320b32b3cc5c05424eeb3d94007f690aba67a

Transactions (1)

Coinbase72a16e2e33d0fe…4007f690aba67a

1 in → 1 out9.5800 XPM116 B

AbwWkWZt…kawDhufa

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.

1.662 × 10¹⁰³(104-digit number)

16621440111105370940…68755969558818324479

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

1.662 × 10¹⁰³(104-digit number)

16621440111105370940…68755969558818324479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.662 × 10¹⁰³(104-digit number)

16621440111105370940…68755969558818324481

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

3.324 × 10¹⁰³(104-digit number)

33242880222210741881…37511939117636648959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.324 × 10¹⁰³(104-digit number)

33242880222210741881…37511939117636648961

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

6.648 × 10¹⁰³(104-digit number)

66485760444421483762…75023878235273297919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.648 × 10¹⁰³(104-digit number)

66485760444421483762…75023878235273297921

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

1.329 × 10¹⁰⁴(105-digit number)

13297152088884296752…50047756470546595839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.329 × 10¹⁰⁴(105-digit number)

13297152088884296752…50047756470546595841

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

2.659 × 10¹⁰⁴(105-digit number)

26594304177768593504…00095512941093191679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.659 × 10¹⁰⁴(105-digit number)

26594304177768593504…00095512941093191681

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