Block #238,651

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 4:06:54 PM · Difficulty 9.9529 · 6,571,071 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d32c4a5dc912bd21eb8f6b4db57b202d5a58838d748d990ce24dec229a831fd5

View on Chainz ↗

Height

#238,651

Difficulty

9.952866

Transactions

Size

1.84 KB

Version

Bits

09f3ef0f

Nonce

25,845

Timestamp

11/1/2013, 4:06:54 PM

Confirmations

6,571,071

Mined by

⛏️ ;Rs+AKfwt5JYHvbU43cJZsmFAbyqP2jsjT5QJQ

Merkle Root

b89f5ba96ffd36b9561288a008379393cc17d1ac172573efa5119a07bacfb294

Transactions (1)

Coinbaseb89f5ba96ffd36…119a07bacfb294

1 in → 51 out10.0600 XPM1.75 KB

AKfwt5JY…jsjT5QJQ AdnG9gQ7…N9B7mA2p ANuKx9Ke…wm7nrBRq AQtzUSwq…htAuF3yC AcEnwywz…vZtt2xTs

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.

4.789 × 10⁹²(93-digit number)

47890865709066382178…10772939255192959999

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

4.789 × 10⁹²(93-digit number)

47890865709066382178…10772939255192959999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.789 × 10⁹²(93-digit number)

47890865709066382178…10772939255192960001

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

9.578 × 10⁹²(93-digit number)

95781731418132764356…21545878510385919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.578 × 10⁹²(93-digit number)

95781731418132764356…21545878510385920001

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

1.915 × 10⁹³(94-digit number)

19156346283626552871…43091757020771839999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.915 × 10⁹³(94-digit number)

19156346283626552871…43091757020771840001

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

3.831 × 10⁹³(94-digit number)

38312692567253105742…86183514041543679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.831 × 10⁹³(94-digit number)

38312692567253105742…86183514041543680001

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

7.662 × 10⁹³(94-digit number)

76625385134506211484…72367028083087359999

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 #238,651

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