Block #230,824

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 1:28:55 AM · Difficulty 9.9400 · 6,575,686 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc10dafbfc0967286638f29b7ba9cae68eb67224446b42eccfc0d9442f4db06b

View on Chainz ↗

Height

#230,824

Difficulty

9.939962

Transactions

Size

3.97 KB

Version

Bits

09f0a15d

Nonce

21,759

Timestamp

10/28/2013, 1:28:55 AM

Confirmations

6,575,686

Mined by

⛏️ P2SHALB921FLePptpVQPQGkeSThEndsSbwbjXN

Merkle Root

3417869812de836a56e6db1c0caa4f986a21040e12b3c590e2b07ea34611451e

Transactions (4)

Coinbase2ac023fc1a4783…cca0939f3618c1

1 in → 1 out10.1798 XPM109 B

ALB921FL…sSbwbjXN

c8c907c1060900…5e653ecd2bb99e

1 in → 2 out212.3661 XPM226 B

AboBRoQN…McKuBEnW AZKmfrhC…ceScw5zj

ba0ac145bc0468…90232682e42b92

1 in → 2 out10.1400 XPM192 B

AQAvQSWZ…C9mFkvux AZZGx6eL…qKffi59Q

0fb5b30bcccd0f…0b89632f12ccca

23 in → 1 out2.2600 XPM3.37 KB

AdGTHfkW…Pe269GoE

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.

1.395 × 10⁹³(94-digit number)

13954027240155607513…52690797599321453999

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

1.395 × 10⁹³(94-digit number)

13954027240155607513…52690797599321453999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.395 × 10⁹³(94-digit number)

13954027240155607513…52690797599321454001

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

2.790 × 10⁹³(94-digit number)

27908054480311215027…05381595198642907999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.790 × 10⁹³(94-digit number)

27908054480311215027…05381595198642908001

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

5.581 × 10⁹³(94-digit number)

55816108960622430055…10763190397285815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.581 × 10⁹³(94-digit number)

55816108960622430055…10763190397285816001

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

1.116 × 10⁹⁴(95-digit number)

11163221792124486011…21526380794571631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.116 × 10⁹⁴(95-digit number)

11163221792124486011…21526380794571632001

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

2.232 × 10⁹⁴(95-digit number)

22326443584248972022…43052761589143263999

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 #230,824

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