Block #490,919

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 4:13:03 AM · Difficulty 10.6800 · 6,325,893 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f809dd82d90a07b1647513b557d5c3071dc51b48c354a56494af961cfeb932c9

View on Chainz ↗

Height

#490,919

Difficulty

10.680000

Transactions

Size

935 B

Version

Bits

0aae1475

Nonce

6,151

Timestamp

4/14/2014, 4:13:03 AM

Confirmations

6,325,893

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

09282c322e7ffeec018f0c2248c366fe840807cb8e51caa7d873b89a6ac04bcb

Transactions (1)

Coinbase09282c322e7ffe…73b89a6ac04bcb

1 in → 23 out8.7500 XPM845 B

AdFLJFhb…bsaVkAyh AUFKXvnz…342ApNcm AGz9gyZW…bo8NYQpw AXCpMYgL…1r94ZQDa AXVLciVJ…uTVo9CdN

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.

4.999 × 10⁹³(94-digit number)

49992246568170123551…64446118976466269999

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

4.999 × 10⁹³(94-digit number)

49992246568170123551…64446118976466269999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.999 × 10⁹³(94-digit number)

49992246568170123551…64446118976466270001

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

9.998 × 10⁹³(94-digit number)

99984493136340247103…28892237952932539999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.998 × 10⁹³(94-digit number)

99984493136340247103…28892237952932540001

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

1.999 × 10⁹⁴(95-digit number)

19996898627268049420…57784475905865079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.999 × 10⁹⁴(95-digit number)

19996898627268049420…57784475905865080001

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

3.999 × 10⁹⁴(95-digit number)

39993797254536098841…15568951811730159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.999 × 10⁹⁴(95-digit number)

39993797254536098841…15568951811730160001

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

7.998 × 10⁹⁴(95-digit number)

79987594509072197682…31137903623460319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.998 × 10⁹⁴(95-digit number)

79987594509072197682…31137903623460320001

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 #490,919

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