Block #180,703

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/26/2013, 12:22:56 AM · Difficulty 9.8620 · 6,625,315 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a43c50227357be4cd41c6ae56d1cf8cde0bc2e03d40fdef8bb40b60e401c862

View on Chainz ↗

Height

#180,703

Difficulty

9.861984

Transactions

Size

1.01 KB

Version

Bits

09dcaafc

Nonce

654,090

Timestamp

9/26/2013, 12:22:56 AM

Confirmations

6,625,315

Mined by

⛏️ P2SHASgiASPpnemBb4MeFdgraqVqsu8oTLBwx4

Merkle Root

39cba9b95a28ed26d1c355796a167eaeb9a406e3e4ba14819b265b9588a47e0d

Transactions (5)

Coinbase279f1b5a7bb31c…a905c1b4dcbb07

1 in → 1 out10.3100 XPM109 B

ASgiASPp…8oTLBwx4

3bddefc0ebbdd0…33b81abdc1c347

1 in → 1 out10.2500 XPM158 B

AN7CTbAY…CXZXPsEU

dd93d85aa8d222…4667330c9e42f8

1 in → 2 out10.2500 XPM227 B

AZ3KGNVk…ADtqeBiM ASf1waS6…phfxS8Bv

fe8cc0d6ad3ef9…ce302b86bf1b63

1 in → 2 out10.2500 XPM225 B

AcPouoLt…vS3yrcwQ AUpuXFAT…CHtqSpM8

52180154e4a5aa…672f78c7fffb52

1 in → 2 out10.2500 XPM226 B

AMY4QdNd…9VsXWgBF AdWp2YRv…FDtt217a

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.

7.229 × 10⁹⁵(96-digit number)

72296088008695792061…83839992890074300799

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

7.229 × 10⁹⁵(96-digit number)

72296088008695792061…83839992890074300799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.229 × 10⁹⁵(96-digit number)

72296088008695792061…83839992890074300801

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

1.445 × 10⁹⁶(97-digit number)

14459217601739158412…67679985780148601599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.445 × 10⁹⁶(97-digit number)

14459217601739158412…67679985780148601601

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

2.891 × 10⁹⁶(97-digit number)

28918435203478316824…35359971560297203199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.891 × 10⁹⁶(97-digit number)

28918435203478316824…35359971560297203201

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

5.783 × 10⁹⁶(97-digit number)

57836870406956633649…70719943120594406399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.783 × 10⁹⁶(97-digit number)

57836870406956633649…70719943120594406401

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

1.156 × 10⁹⁷(98-digit number)

11567374081391326729…41439886241188812799

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