Block #304,825

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 3:28:03 AM · Difficulty 9.9935 · 6,502,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c38b383434cb4b9d46561b44bbd516e3b337791ecf28751183361018adf1daa9

View on Chainz ↗

Height

#304,825

Difficulty

9.993453

Transactions

Size

1.96 KB

Version

Bits

09fe52ea

Nonce

158,888

Timestamp

12/11/2013, 3:28:03 AM

Confirmations

6,502,757

Mined by

⛏️ aRAKZyToQzGJfXjFvhJAhk8xzuKsGwumbjQw

Merkle Root

a0eafc83664b645982f4aede9346f70c10b31dc35341b16b838d063eb7209bf0

Transactions (4)

Coinbasef5aee50bfb5282…1e048cfb11ef4b

1 in → 30 out9.9800 XPM1.06 KB

AKZyToQz…GwumbjQw AUJvPysZ…LPjjpN9v Ad9pSzHt…cpJ3y2zz AGE8rQ1i…v89jQZhq AWXYBWKP…qQAoisBJ

64b978667cc502…c27952c1e12375

1 in → 2 out5.8554 XPM227 B

ALcv5G2y…NWtyyh6e AU8Gy4Na…7NpS8keC

2dc1e7f71c8add…c763bc6086b580

1 in → 2 out4.8141 XPM227 B

AVSSoqRA…aFjFn3Zm ATCU6k8Y…Y64nYJax

2e0e7cb900f3ed…ebdc331e7fbdde

2 in → 2 out1.2360 XPM376 B

AUdCK6Rx…zYKX1p4W AZwyMUeE…rxMQeLU7

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.

8.113 × 10⁹³(94-digit number)

81134662509319756767…21800733736801566639

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

8.113 × 10⁹³(94-digit number)

81134662509319756767…21800733736801566639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.113 × 10⁹³(94-digit number)

81134662509319756767…21800733736801566641

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

1.622 × 10⁹⁴(95-digit number)

16226932501863951353…43601467473603133279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.622 × 10⁹⁴(95-digit number)

16226932501863951353…43601467473603133281

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

3.245 × 10⁹⁴(95-digit number)

32453865003727902706…87202934947206266559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.245 × 10⁹⁴(95-digit number)

32453865003727902706…87202934947206266561

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

6.490 × 10⁹⁴(95-digit number)

64907730007455805413…74405869894412533119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.490 × 10⁹⁴(95-digit number)

64907730007455805413…74405869894412533121

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

1.298 × 10⁹⁵(96-digit number)

12981546001491161082…48811739788825066239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.298 × 10⁹⁵(96-digit number)

12981546001491161082…48811739788825066241

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 #304,825

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