Block #1,432,944

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2016, 2:11:38 PM · Difficulty 10.7916 · 5,404,163 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad46313df45e9cc273371cbe8bd61d76b47be04125d6f3825291524ef2581f50

View on Chainz ↗

Height

#1,432,944

Difficulty

10.791552

Transactions

Size

4.75 KB

Version

Bits

0acaa321

Nonce

297,121,809

Timestamp

1/28/2016, 2:11:38 PM

Confirmations

5,404,163

Mined by

⛏️ P2SHATAfyqVU3ipBrQynBdvdJF6JbwVKsacHNh

Merkle Root

7fc2dd748ebc1eaef9a0b83abfa1d6e96e0a28cc102e9f5aafbfc048486f20a0

Transactions (2)

Coinbaseb92e7bb6a251c6…4663370360ade3

1 in → 1 out8.6200 XPM110 B

ATAfyqVU…VKsacHNh

b1fb6db08307f9…7aa7f327d7cc93

31 in → 2 out2230.8900 XPM4.55 KB

AQzJc3be…EGfgCMXJ AbbDhji6…WASSsNA3

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.

9.501 × 10⁹⁶(97-digit number)

95011189730114406899…18822701033608478719

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

9.501 × 10⁹⁶(97-digit number)

95011189730114406899…18822701033608478719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.501 × 10⁹⁶(97-digit number)

95011189730114406899…18822701033608478721

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

1.900 × 10⁹⁷(98-digit number)

19002237946022881379…37645402067216957439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.900 × 10⁹⁷(98-digit number)

19002237946022881379…37645402067216957441

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

3.800 × 10⁹⁷(98-digit number)

38004475892045762759…75290804134433914879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.800 × 10⁹⁷(98-digit number)

38004475892045762759…75290804134433914881

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

7.600 × 10⁹⁷(98-digit number)

76008951784091525519…50581608268867829759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.600 × 10⁹⁷(98-digit number)

76008951784091525519…50581608268867829761

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

1.520 × 10⁹⁸(99-digit number)

15201790356818305103…01163216537735659519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.520 × 10⁹⁸(99-digit number)

15201790356818305103…01163216537735659521

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

Block #1,432,944

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