Block #218,711

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 2:25:11 AM · Difficulty 9.9311 · 6,576,828 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f4b817f02edfb987b84322edfac58d06e219aed2f9e58eeca58eca547a970cf

View on Chainz ↗

Height

#218,711

Difficulty

9.931103

Transactions

Size

968 B

Version

Bits

09ee5cc1

Nonce

40,022

Timestamp

10/20/2013, 2:25:11 AM

Confirmations

6,576,828

Mined by

⛏️ P2SHAU1AuZS4tL1K9MmiS6roLmEZQKTb8WMczp

Merkle Root

5eaf4e823c54597d0fc9bf3777f5d9e5ce802a4e2245d691cb4e8e502ed6eba6

Transactions (2)

Coinbase8d02f51f374566…63ca95d3f77152

1 in → 1 out10.1300 XPM109 B

AU1AuZS4…Tb8WMczp

2f1751d4d14a6c…812b90e59cec50

4 in → 9 out40.5800 XPM771 B

AWk3tNVN…AM1VtV3G AN64hFft…9qqgSHo4 AMuPGPXT…eMMNvd8v AHxSrokp…PAydPZRV AU5g73DE…hY8WccpK

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.

3.962 × 10⁹⁰(91-digit number)

39622273597537776803…50630446162947880319

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

3.962 × 10⁹⁰(91-digit number)

39622273597537776803…50630446162947880319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.962 × 10⁹⁰(91-digit number)

39622273597537776803…50630446162947880321

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

7.924 × 10⁹⁰(91-digit number)

79244547195075553606…01260892325895760639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.924 × 10⁹⁰(91-digit number)

79244547195075553606…01260892325895760641

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

1.584 × 10⁹¹(92-digit number)

15848909439015110721…02521784651791521279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.584 × 10⁹¹(92-digit number)

15848909439015110721…02521784651791521281

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

3.169 × 10⁹¹(92-digit number)

31697818878030221442…05043569303583042559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.169 × 10⁹¹(92-digit number)

31697818878030221442…05043569303583042561

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

6.339 × 10⁹¹(92-digit number)

63395637756060442885…10087138607166085119

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