Block #214,490

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 12:48:29 PM · Difficulty 9.9232 · 6,603,343 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d2e01c67a892f36638bb0a5178c54daf5ae9beb21ea50daae74f2550361db30

View on Chainz ↗

Height

#214,490

Difficulty

9.923247

Transactions

Size

5.06 KB

Version

Bits

09ec59ee

Nonce

1,164,765,551

Timestamp

10/17/2013, 12:48:29 PM

Confirmations

6,603,343

Mined by

⛏️ ER_AGbRhLj1HQi4pXYvW1G5HRrmefnZcEQFqQ

Merkle Root

791d2d3662a9c5cf966784f04ba36eca32b13edf6dfae0e29872e24bb1e3ba27

Transactions (1)

Coinbase791d2d3662a9c5…72e24bb1e3ba27

1 in → 148 out10.0800 XPM4.97 KB

AGbRhLj1…nZcEQFqQ AGHsFFzK…3J7QNqtQ ANnERhAg…PWEtxxVs AQ9mcAM7…xAF4qFjc AGKDHDYN…e4dh3GPV

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.

2.470 × 10⁹⁰(91-digit number)

24708244188640848956…17023882569592509439

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

2.470 × 10⁹⁰(91-digit number)

24708244188640848956…17023882569592509439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.470 × 10⁹⁰(91-digit number)

24708244188640848956…17023882569592509441

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

4.941 × 10⁹⁰(91-digit number)

49416488377281697913…34047765139185018879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.941 × 10⁹⁰(91-digit number)

49416488377281697913…34047765139185018881

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

9.883 × 10⁹⁰(91-digit number)

98832976754563395827…68095530278370037759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.883 × 10⁹⁰(91-digit number)

98832976754563395827…68095530278370037761

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

1.976 × 10⁹¹(92-digit number)

19766595350912679165…36191060556740075519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.976 × 10⁹¹(92-digit number)

19766595350912679165…36191060556740075521

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

3.953 × 10⁹¹(92-digit number)

39533190701825358330…72382121113480151039

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 #214,490

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