Block #167,868

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/16/2013, 10:03:49 PM · Difficulty 9.8682 · 6,641,149 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ec570c85a82d576a4c295c4d5ed0d0dd039dc5009c179f3142f7ece83ec295a

View on Chainz ↗

Height

#167,868

Difficulty

9.868175

Transactions

Size

812 B

Version

Bits

09de40bc

Nonce

81,061

Timestamp

9/16/2013, 10:03:49 PM

Confirmations

6,641,149

Mined by

⛏️ P2SHALC5XoYKkKbT2nJELyBm6AKYYYocQRuX8L

Merkle Root

dd221270dc7ad1f6ba86fdc81ad302453f209272697e18271348a86cf0eb9e19

Transactions (3)

Coinbase2f558ea5e366d4…e4cd1daa6528bc

1 in → 1 out10.2700 XPM109 B

ALC5XoYK…ocQRuX8L

9e04d3a01aaf7a…026122b11d8187

3 in → 1 out30.8000 XPM388 B

Abg9b4kX…im9CLs7g

2588f3d7a83058…1f2c09a204c106

1 in → 2 out2.1110 XPM226 B

ANq6Hy7m…86xjrm8N Adhttbhc…9i1za24v

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.

4.443 × 10⁹¹(92-digit number)

44438133858043466385…29673499532827077879

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

4.443 × 10⁹¹(92-digit number)

44438133858043466385…29673499532827077879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.443 × 10⁹¹(92-digit number)

44438133858043466385…29673499532827077881

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

8.887 × 10⁹¹(92-digit number)

88876267716086932770…59346999065654155759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.887 × 10⁹¹(92-digit number)

88876267716086932770…59346999065654155761

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

1.777 × 10⁹²(93-digit number)

17775253543217386554…18693998131308311519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.777 × 10⁹²(93-digit number)

17775253543217386554…18693998131308311521

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

3.555 × 10⁹²(93-digit number)

35550507086434773108…37387996262616623039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.555 × 10⁹²(93-digit number)

35550507086434773108…37387996262616623041

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

7.110 × 10⁹²(93-digit number)

71101014172869546216…74775992525233246079

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

Block #167,868

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