Block #238,883

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 6:51:05 PM · Difficulty 9.9535 · 6,562,207 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0995f3c9edefb4a047bdb9b411e553cbf4836b0d0f3d0c6da74273ff5fdc69c

View on Chainz ↗

Height

#238,883

Difficulty

9.953485

Transactions

Size

2.04 KB

Version

Bits

09f4179f

Nonce

89,777

Timestamp

11/1/2013, 6:51:05 PM

Confirmations

6,562,207

Mined by

⛏️ #RsARpndEmcGyFUFhdFVbgqJiPBAmHg792kEk

Merkle Root

6639dbaa8ad7b54424a15000ee1f6cf4680b5693a438897ab96b5968f8c3aea7

Transactions (1)

Coinbase6639dbaa8ad7b5…6b5968f8c3aea7

1 in → 57 out10.0600 XPM1.95 KB

ARpndEmc…Hg792kEk AbeUZSvK…ijGzuyjz 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.

2.896 × 10⁹²(93-digit number)

28962047865195383451…69137572069216244079

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

2.896 × 10⁹²(93-digit number)

28962047865195383451…69137572069216244079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.896 × 10⁹²(93-digit number)

28962047865195383451…69137572069216244081

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

5.792 × 10⁹²(93-digit number)

57924095730390766902…38275144138432488159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.792 × 10⁹²(93-digit number)

57924095730390766902…38275144138432488161

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

1.158 × 10⁹³(94-digit number)

11584819146078153380…76550288276864976319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.158 × 10⁹³(94-digit number)

11584819146078153380…76550288276864976321

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

2.316 × 10⁹³(94-digit number)

23169638292156306760…53100576553729952639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.316 × 10⁹³(94-digit number)

23169638292156306760…53100576553729952641

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

4.633 × 10⁹³(94-digit number)

46339276584312613521…06201153107459905279

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