Block #494,848

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 8:56:13 AM · Difficulty 10.7262 · 6,299,398 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2aed01fa86724f3b84aad6afae45a9521acf67e320f003acdeb6f06b338e8210

View on Chainz ↗

Height

#494,848

Difficulty

10.726192

Transactions

Size

1.41 KB

Version

Bits

0ab9e7be

Nonce

275,014,528

Timestamp

4/16/2014, 8:56:13 AM

Confirmations

6,299,398

Merkle Root

8a6970f8537ad4e0721e004a7cb5c1aa498b0eab73818aa7b5f62e825fdea97f

Transactions (5)

Coinbasee03ddf1ff930d2…031f4be028ff34

1 in → 1 out8.7200 XPM116 B

AbwWkWZt…kawDhufa

9c5b4d63ce5888…de37fb847eb7d6

3 in → 4 out9.1675 XPM556 B

Aai7rmvE…JWhtS5Q5 AeKNrjNj…1NEq95Ta AZH3aBJB…T7FVgZ83 AL7UX3yh…XePJXGnn

f8a1ef34b5eac5…b9371356a71c4b

1 in → 2 out5.6813 XPM225 B

ASRQFbkA…GhdhgzeC AaRzDysT…7GHngFkH

a5ec9c0cd11bc5…148b3cd62634d8

1 in → 2 out4.2944 XPM226 B

AZf4XWkX…Lfz4oE4Q AWLb3YUt…ir3KYZS1

4993327cd21f4f…f72c22bdde283d

1 in → 2 out3.5033 XPM226 B

AJMnxSJD…g744rVTy AdqH4QjD…3vhGVHG4

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.

1.730 × 10⁹⁷(98-digit number)

17300304361562593514…89497931520680061999

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

1.730 × 10⁹⁷(98-digit number)

17300304361562593514…89497931520680061999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.730 × 10⁹⁷(98-digit number)

17300304361562593514…89497931520680062001

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

3.460 × 10⁹⁷(98-digit number)

34600608723125187029…78995863041360123999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.460 × 10⁹⁷(98-digit number)

34600608723125187029…78995863041360124001

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

6.920 × 10⁹⁷(98-digit number)

69201217446250374059…57991726082720247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.920 × 10⁹⁷(98-digit number)

69201217446250374059…57991726082720248001

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

1.384 × 10⁹⁸(99-digit number)

13840243489250074811…15983452165440495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.384 × 10⁹⁸(99-digit number)

13840243489250074811…15983452165440496001

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

2.768 × 10⁹⁸(99-digit number)

27680486978500149623…31966904330880991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.768 × 10⁹⁸(99-digit number)

27680486978500149623…31966904330880992001

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