Block #359,226

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/14/2014, 3:28:55 PM · Difficulty 10.3880 · 6,433,237 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e3bf0714145623ab63ddd15264c5409ccb65d9e0c904819d048d50f8b47e94a3

View on Chainz ↗

Height

#359,226

Difficulty

10.387966

Transactions

Size

952 B

Version

Bits

0a6351c3

Nonce

345,339

Timestamp

1/14/2014, 3:28:55 PM

Confirmations

6,433,237

Merkle Root

e6c345344d0e8d41ec66875a8aefe3d80427e81f96d0c3345eca3560b7018348

Transactions (3)

Coinbasefb78fda36c885c…68a159170a9e8f

1 in → 1 out9.2700 XPM110 B

AeKNrjNj…1NEq95Ta

563c73dceeabad…9a305c6b5c29b2

1 in → 2 out7.9800 XPM225 B

AVLTe17z…YZjG3pgV AVkWEqrf…XRpY7mG7

2540bb4b9e163f…e8265eece781b3

3 in → 2 out19.4821 XPM524 B

AWWhvxi5…VXKJ5fHo AVWTuF2g…JyhYqGF5

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.

5.352 × 10¹⁰⁰(101-digit number)

53523046575280689932…77846514688360110079

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

5.352 × 10¹⁰⁰(101-digit number)

53523046575280689932…77846514688360110079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.352 × 10¹⁰⁰(101-digit number)

53523046575280689932…77846514688360110081

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

1.070 × 10¹⁰¹(102-digit number)

10704609315056137986…55693029376720220159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.070 × 10¹⁰¹(102-digit number)

10704609315056137986…55693029376720220161

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

2.140 × 10¹⁰¹(102-digit number)

21409218630112275973…11386058753440440319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.140 × 10¹⁰¹(102-digit number)

21409218630112275973…11386058753440440321

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

4.281 × 10¹⁰¹(102-digit number)

42818437260224551946…22772117506880880639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.281 × 10¹⁰¹(102-digit number)

42818437260224551946…22772117506880880641

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

8.563 × 10¹⁰¹(102-digit number)

85636874520449103892…45544235013761761279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.563 × 10¹⁰¹(102-digit number)

85636874520449103892…45544235013761761281

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