Block #232,351

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/29/2013, 1:29:21 AM · Difficulty 9.9411 · 6,563,292 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

954d19023819b37d08ce6bf10e2655d9165bf10f2e585777a6db90b3326c253a

View on Chainz ↗

Height

#232,351

Difficulty

9.941075

Transactions

Size

651 B

Version

Bits

09f0ea52

Nonce

98,050

Timestamp

10/29/2013, 1:29:21 AM

Confirmations

6,563,292

Mined by

⛏️ P2SHAUUDNVMK1hKxPHK7xQhjYKG4Esr4MfPsLk

Merkle Root

4a5118f6e192c21bd53655945e508695bb9c207a5de8d1ad6c585b2f737f2112

Transactions (3)

Coinbase6d8779a44cb8b3…82cd1ea6623040

1 in → 1 out10.1200 XPM109 B

AUUDNVMK…r4MfPsLk

8bffba42a6dfe5…2615cceecdf273

1 in → 2 out6.0002 XPM226 B

AVyDnEgr…5LH25LTT AH3dDrPX…iXBYe8ZV

847b4f33ef51d6…a1811fd33711fe

1 in → 2 out5.1786 XPM226 B

AU7bLduJ…b1yVKUGA AJbrcWEe…3NF4ZpaN

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.

4.862 × 10⁹⁵(96-digit number)

48621749114184586856…53948886446584783999

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

4.862 × 10⁹⁵(96-digit number)

48621749114184586856…53948886446584783999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.862 × 10⁹⁵(96-digit number)

48621749114184586856…53948886446584784001

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

9.724 × 10⁹⁵(96-digit number)

97243498228369173713…07897772893169567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.724 × 10⁹⁵(96-digit number)

97243498228369173713…07897772893169568001

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

1.944 × 10⁹⁶(97-digit number)

19448699645673834742…15795545786339135999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.944 × 10⁹⁶(97-digit number)

19448699645673834742…15795545786339136001

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

3.889 × 10⁹⁶(97-digit number)

38897399291347669485…31591091572678271999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.889 × 10⁹⁶(97-digit number)

38897399291347669485…31591091572678272001

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

7.779 × 10⁹⁶(97-digit number)

77794798582695338970…63182183145356543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.779 × 10⁹⁶(97-digit number)

77794798582695338970…63182183145356544001

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