Block #233,326

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/29/2013, 3:43:26 PM · Difficulty 9.9425 · 6,561,257 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32da824f3a8865453c8325a2e6536047dff8cc7334e19011b7fe97a2a3e4067d

View on Chainz ↗

Height

#233,326

Difficulty

9.942506

Transactions

Size

808 B

Version

Bits

09f14813

Nonce

11,105

Timestamp

10/29/2013, 3:43:26 PM

Confirmations

6,561,257

Mined by

⛏️ P2SHAH8MuWecApb7HmsNwfd9UPDw7y2bVG62mK

Merkle Root

815630304c41519640818a9616221da86c257da64b9e09c26dbcc273f55667c5

Transactions (4)

Coinbasebe8cde83ac4bb8…2688b25bd7dc0b

1 in → 1 out10.1300 XPM109 B

AH8MuWec…2bVG62mK

aabf1c902c50d4…34aec51100d1e0

1 in → 2 out10.1200 XPM191 B

AL3P2QDv…gbbaSnCj AbNFNbRy…6mZj5ndZ

fa367ab44f5b2d…0fcd95d99c589d

1 in → 1 out2.9273 XPM192 B

AXhMcKBp…Drzdc8Hw

eae90d2a5389f7…f262026a18066a

1 in → 2 out4.9669 XPM227 B

AdCbHMuV…xwQmtx9z AWWoSRFz…jheQtJHw

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.

6.106 × 10⁹²(93-digit number)

61063367976737565285…23697018454278422659

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

6.106 × 10⁹²(93-digit number)

61063367976737565285…23697018454278422659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.106 × 10⁹²(93-digit number)

61063367976737565285…23697018454278422661

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

1.221 × 10⁹³(94-digit number)

12212673595347513057…47394036908556845319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.221 × 10⁹³(94-digit number)

12212673595347513057…47394036908556845321

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

2.442 × 10⁹³(94-digit number)

24425347190695026114…94788073817113690639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.442 × 10⁹³(94-digit number)

24425347190695026114…94788073817113690641

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

4.885 × 10⁹³(94-digit number)

48850694381390052228…89576147634227381279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.885 × 10⁹³(94-digit number)

48850694381390052228…89576147634227381281

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

9.770 × 10⁹³(94-digit number)

97701388762780104457…79152295268454762559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.770 × 10⁹³(94-digit number)

97701388762780104457…79152295268454762561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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