Block #1,032,961

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/26/2015, 2:43:29 AM · Difficulty 10.7515 · 5,800,934 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f950fd5b6963094711b8a29749baad126286109771a795d8784b4a423dcdcb61

View on Chainz ↗

Height

#1,032,961

Difficulty

10.751519

Transactions

Size

244 B

Version

Bits

0ac06385

Nonce

557,516,696

Timestamp

4/26/2015, 2:43:29 AM

Confirmations

5,800,934

Mined by

⛏️ P2SHAUV3ZXsawxZuaXubcanNHw2sUMP3xQCbyH

Merkle Root

99e943ea51ec5c5cc691d52953243e86877a1450e5516aca6fafb78247e5b1b0

Transactions (1)

Coinbase99e943ea51ec5c…afb78247e5b1b0

1 in → 2 out8.6400 XPM152 B

AUV3ZXsa…P3xQCbyH ALPu3s2c…EJXLjVFh

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.

2.289 × 10⁹⁸(99-digit number)

22892501512305620229…84347574219004764159

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

2.289 × 10⁹⁸(99-digit number)

22892501512305620229…84347574219004764159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.289 × 10⁹⁸(99-digit number)

22892501512305620229…84347574219004764161

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

4.578 × 10⁹⁸(99-digit number)

45785003024611240458…68695148438009528319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.578 × 10⁹⁸(99-digit number)

45785003024611240458…68695148438009528321

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

9.157 × 10⁹⁸(99-digit number)

91570006049222480916…37390296876019056639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.157 × 10⁹⁸(99-digit number)

91570006049222480916…37390296876019056641

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

1.831 × 10⁹⁹(100-digit number)

18314001209844496183…74780593752038113279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.831 × 10⁹⁹(100-digit number)

18314001209844496183…74780593752038113281

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

3.662 × 10⁹⁹(100-digit number)

36628002419688992366…49561187504076226559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.662 × 10⁹⁹(100-digit number)

36628002419688992366…49561187504076226561

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 #1,032,961

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