Block #175,975

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/22/2013, 3:57:03 PM · Difficulty 9.8643 · 6,618,899 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff0fd473e6aad04b758019e747d44b3758231d495dfa95cb72c184f8efcbf6b3

View on Chainz ↗

Height

#175,975

Difficulty

9.864293

Transactions

Size

425 B

Version

Bits

09dd424d

Nonce

73,475

Timestamp

9/22/2013, 3:57:03 PM

Confirmations

6,618,899

Mined by

⛏️ P2SHALefmcuDW4F9iECbUGXjGP8npv6bSfgMPT

Merkle Root

cba8a860c908e3220b1218909e9f6ff0b790fe5dd0cef1420e59c9c229a747ed

Transactions (2)

Coinbase5e6cf205997094…43f43129982586

1 in → 1 out10.2700 XPM109 B

ALefmcuD…6bSfgMPT

715747b558a6a5…e808772f9d5ec1

1 in → 2 out4.1019 XPM227 B

AXwKKGcU…yK2w3TwR AQ6PW3KP…XR5s58KE

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.

4.097 × 10⁹¹(92-digit number)

40979332600939502605…08128973725249574399

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

4.097 × 10⁹¹(92-digit number)

40979332600939502605…08128973725249574399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.097 × 10⁹¹(92-digit number)

40979332600939502605…08128973725249574401

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

8.195 × 10⁹¹(92-digit number)

81958665201879005211…16257947450499148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.195 × 10⁹¹(92-digit number)

81958665201879005211…16257947450499148801

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

1.639 × 10⁹²(93-digit number)

16391733040375801042…32515894900998297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.639 × 10⁹²(93-digit number)

16391733040375801042…32515894900998297601

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

3.278 × 10⁹²(93-digit number)

32783466080751602084…65031789801996595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.278 × 10⁹²(93-digit number)

32783466080751602084…65031789801996595201

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

6.556 × 10⁹²(93-digit number)

65566932161503204169…30063579603993190399

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