Block #483,946

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 8:01:36 AM · Difficulty 10.5740 · 6,322,141 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7952f2534117b09fb4768aa7dcd006f66f1eee090610a5b101b11c0e5c87159

View on Chainz ↗

Height

#483,946

Difficulty

10.573965

Transactions

Size

3.55 KB

Version

Bits

0a92ef65

Nonce

34,195

Timestamp

4/10/2014, 8:01:36 AM

Confirmations

6,322,141

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9a7f990752821f6c5fff5ae0e98d450ba1d25cee7bb6a8a9bbcd5230d5e771fa

Transactions (3)

Coinbase2958e36fc4e589…51d9f823dedbc2

1 in → 1 out8.9759 XPM110 B

AeKNrjNj…1NEq95Ta

f7c96d497d7428…bfbae1a87f033d

17 in → 1 out48.4700 XPM2.50 KB

AJYUUNzY…NnqfpxUt

2fa89e66b755ff…b30d4996145fe6

4 in → 12 out36.1900 XPM873 B

AKYYe3Cm…Ebm4oP9w AGGn2KCs…XgJwJMWz ARBEqonV…m5Bp67tn AeKNrjNj…1NEq95Ta AVFAS6po…steZGPE7

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.

2.442 × 10¹⁰³(104-digit number)

24423216954606849219…32632104093988535039

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

2.442 × 10¹⁰³(104-digit number)

24423216954606849219…32632104093988535039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.442 × 10¹⁰³(104-digit number)

24423216954606849219…32632104093988535041

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

4.884 × 10¹⁰³(104-digit number)

48846433909213698439…65264208187977070079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.884 × 10¹⁰³(104-digit number)

48846433909213698439…65264208187977070081

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

9.769 × 10¹⁰³(104-digit number)

97692867818427396878…30528416375954140159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.769 × 10¹⁰³(104-digit number)

97692867818427396878…30528416375954140161

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

1.953 × 10¹⁰⁴(105-digit number)

19538573563685479375…61056832751908280319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.953 × 10¹⁰⁴(105-digit number)

19538573563685479375…61056832751908280321

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

3.907 × 10¹⁰⁴(105-digit number)

39077147127370958751…22113665503816560639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.907 × 10¹⁰⁴(105-digit number)

39077147127370958751…22113665503816560641

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