Block #494,837

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 8:45:38 AM · Difficulty 10.7263 · 6,298,052 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

19b714e4056d7d35e551e4add1e48c63b32c5a9a9b2d4be8790aeb31f4ba1811

View on Chainz ↗

Height

#494,837

Difficulty

10.726252

Transactions

Size

3.76 KB

Version

Bits

0ab9eba0

Nonce

14,617

Timestamp

4/16/2014, 8:45:38 AM

Confirmations

6,298,052

Merkle Root

b99a2c74a86fa0c839f368038a2985381c00dfcfc41b749efc2d69b00d6b0de8

Transactions (4)

Coinbase218c2577b520f9…3b8be87a65e882

1 in → 20 out8.6800 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR AJtNW28X…Syb4Ph5j

849fb02318c06a…80f9dab9e32c96

15 in → 1 out14.9809 XPM2.21 KB

AGohQ9Ho…S5yoYcfg

957cd7db2e8fde…34fba6d0fe24eb

3 in → 2 out22.7193 XPM523 B

AcpU9jJ6…iVWw9aty AJWUh7G2…9N8iooa9

c8d2791148a328…ef4c1cb36a4684

1 in → 2 out7.1304 XPM226 B

AcNfyX9t…hT5WFcoz ATLTiFeQ…54Ntaa42

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.

1.488 × 10⁹⁶(97-digit number)

14884343926931263287…70886563626198036479

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

1.488 × 10⁹⁶(97-digit number)

14884343926931263287…70886563626198036479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.488 × 10⁹⁶(97-digit number)

14884343926931263287…70886563626198036481

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

2.976 × 10⁹⁶(97-digit number)

29768687853862526574…41773127252396072959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.976 × 10⁹⁶(97-digit number)

29768687853862526574…41773127252396072961

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

5.953 × 10⁹⁶(97-digit number)

59537375707725053149…83546254504792145919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.953 × 10⁹⁶(97-digit number)

59537375707725053149…83546254504792145921

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

1.190 × 10⁹⁷(98-digit number)

11907475141545010629…67092509009584291839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.190 × 10⁹⁷(98-digit number)

11907475141545010629…67092509009584291841

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

2.381 × 10⁹⁷(98-digit number)

23814950283090021259…34185018019168583679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.381 × 10⁹⁷(98-digit number)

23814950283090021259…34185018019168583681

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