Block #170,230

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/18/2013, 3:02:53 PM · Difficulty 9.8657 · 6,633,242 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7f84019894dd81affcaf680e59929fa61fd03be6ef12ec30bd8981a7efa92efc

View on Chainz ↗

Height

#170,230

Difficulty

9.865746

Transactions

Size

577 B

Version

Bits

09dda18f

Nonce

32,377

Timestamp

9/18/2013, 3:02:53 PM

Confirmations

6,633,242

Mined by

⛏️ P2SHAU6QKW8rDqYwcBRfNXXiLBJPXnVJw6HhTn

Merkle Root

05d0e53c3458599932939071c8ee283686d946f1c976beb537d625da35c0d04d

Transactions (2)

Coinbase125d9dc2e3f5bc…c23c0c0830498b

1 in → 1 out10.2700 XPM109 B

AU6QKW8r…VJw6HhTn

ca6bd500a160c9…7380a9e6e0c174

2 in → 2 out179.6114 XPM375 B

ASWV7xMu…QfePVbPN AZefvoLB…NnavnA2n

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.

2.578 × 10¹⁰²(103-digit number)

25785778581658034880…14029323161864913279

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

2.578 × 10¹⁰²(103-digit number)

25785778581658034880…14029323161864913279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.578 × 10¹⁰²(103-digit number)

25785778581658034880…14029323161864913281

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

5.157 × 10¹⁰²(103-digit number)

51571557163316069760…28058646323729826559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.157 × 10¹⁰²(103-digit number)

51571557163316069760…28058646323729826561

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

1.031 × 10¹⁰³(104-digit number)

10314311432663213952…56117292647459653119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.031 × 10¹⁰³(104-digit number)

10314311432663213952…56117292647459653121

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

2.062 × 10¹⁰³(104-digit number)

20628622865326427904…12234585294919306239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.062 × 10¹⁰³(104-digit number)

20628622865326427904…12234585294919306241

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

4.125 × 10¹⁰³(104-digit number)

41257245730652855808…24469170589838612479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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