Block #480,486

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 8:22:18 AM · Difficulty 10.5172 · 6,333,726 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f62cc8333e3feb8fcbeb7cc41efcc50191859a3d54860d3cd118aaa74d62fd6

View on Chainz ↗

Height

#480,486

Difficulty

10.517217

Transactions

Size

1.37 KB

Version

Bits

0a846851

Nonce

10,139

Timestamp

4/8/2014, 8:22:18 AM

Confirmations

6,333,726

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a9856a30a5ff8c6deb2916a136ee7135768c7f3d31a168164f04f800bd8d950b

Transactions (5)

Coinbase3a9027f0e1abc0…0f59cbb6685f66

1 in → 1 out9.0700 XPM110 B

AeKNrjNj…1NEq95Ta

84567a01a1bf34…6c9b5f3c3afcaf

2 in → 2 out12.4278 XPM373 B

AaSZ2ZcJ…Ryw6vXQ3 ALdbzuwY…T4dbrNUE

79bff898f4785f…55475605e302d4

2 in → 2 out10.2643 XPM373 B

AS1r7uYt…mqMXGCwP ASANrFq4…fZrzAm1S

009de6c62d7dd5…7c0754056361c4

1 in → 2 out6.5595 XPM225 B

AX8prNPL…m5DXD2f4 AV8zVw1A…g6JcFvdi

813bf69fc8ee55…5c0bf63cc13d9a

1 in → 2 out6.8679 XPM226 B

ANGFtv7Y…82ceDDLy ASzLTHfH…G1ixxG2V

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.

1.266 × 10⁹⁹(100-digit number)

12663193576768072641…27005154781378457599

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

1.266 × 10⁹⁹(100-digit number)

12663193576768072641…27005154781378457599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.266 × 10⁹⁹(100-digit number)

12663193576768072641…27005154781378457601

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

2.532 × 10⁹⁹(100-digit number)

25326387153536145282…54010309562756915199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.532 × 10⁹⁹(100-digit number)

25326387153536145282…54010309562756915201

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

5.065 × 10⁹⁹(100-digit number)

50652774307072290565…08020619125513830399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.065 × 10⁹⁹(100-digit number)

50652774307072290565…08020619125513830401

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

1.013 × 10¹⁰⁰(101-digit number)

10130554861414458113…16041238251027660799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.013 × 10¹⁰⁰(101-digit number)

10130554861414458113…16041238251027660801

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

2.026 × 10¹⁰⁰(101-digit number)

20261109722828916226…32082476502055321599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.026 × 10¹⁰⁰(101-digit number)

20261109722828916226…32082476502055321601

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 #480,486

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