Block #175,896

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/22/2013, 2:33:47 PM · Difficulty 9.8645 · 6,632,034 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd4680ffcddf0fa641909456401f082a22bcd1ebfa347893b0952cd62a52635f

View on Chainz ↗

Height

#175,896

Difficulty

9.864466

Transactions

Size

584 B

Version

Bits

09dd4da8

Nonce

340,217

Timestamp

9/22/2013, 2:33:47 PM

Confirmations

6,632,034

Mined by

⛏️ P2SHAM1A9CZLPnH51axL7hPRTWjkm6as4Lpogj

Merkle Root

472cd1363e4eba02d3dfe0e0be8363abd20c5a48ed0c733990498f6c965baedf

Transactions (3)

Coinbase31b6ab241a7223…565abf8fca1cf3

1 in → 1 out10.2800 XPM109 B

AM1A9CZL…as4Lpogj

28c1f9493426c8…07caf4a633108b

1 in → 1 out10.2500 XPM158 B

ATrGqBKA…Ev1i3JEB

cf972b2689db27…4effd5294a61a3

1 in → 2 out8.2394 XPM227 B

AVnV7AEi…ABqWQfyc Aa6TgyzK…iAg5sRvg

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.

5.137 × 10⁹⁵(96-digit number)

51375676960168451981…66463297105579934719

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

5.137 × 10⁹⁵(96-digit number)

51375676960168451981…66463297105579934719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.137 × 10⁹⁵(96-digit number)

51375676960168451981…66463297105579934721

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

1.027 × 10⁹⁶(97-digit number)

10275135392033690396…32926594211159869439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.027 × 10⁹⁶(97-digit number)

10275135392033690396…32926594211159869441

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

2.055 × 10⁹⁶(97-digit number)

20550270784067380792…65853188422319738879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.055 × 10⁹⁶(97-digit number)

20550270784067380792…65853188422319738881

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

4.110 × 10⁹⁶(97-digit number)

41100541568134761585…31706376844639477759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.110 × 10⁹⁶(97-digit number)

41100541568134761585…31706376844639477761

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

8.220 × 10⁹⁶(97-digit number)

82201083136269523171…63412753689278955519

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

Block #175,896

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