Block #456,239

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 2:18:09 AM · Difficulty 10.4166 · 6,336,339 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2de2b865acc33d4b03e8b6fddc89c171c22cd94ed4800f34760f570cc7e73131

View on Chainz ↗

Height

#456,239

Difficulty

10.416577

Transactions

Size

2.78 KB

Version

Bits

0a6aa4cd

Nonce

43,919

Timestamp

3/23/2014, 2:18:09 AM

Confirmations

6,336,339

Merkle Root

bbd3f1a31c9ea3083cf49d3d5bbc2eb61b88f840f7cccb1cee42e20fe1257755

Transactions (5)

Coinbase71558ed11605d3…45de594bc80475

1 in → 1 out9.2500 XPM109 B

Ab4KAuhy…Ur2GsZAX

f03b8b9294bbd1…af787d95fda020

1 in → 6 out23.9669 XPM362 B

ALRiJagz…NiAKht4v AerL35yq…gE1jPnhy AYmXDTRZ…RjoLiimC AJiUWmxX…BMH9Vzvt AQe12e3Z…HeWcXVsQ

ddabbd8bd40aae…5cdcc43ede5d1b

6 in → 2 out23.9936 XPM966 B

APZdPgPj…7nbJ8XhR ANZAeEP3…88eqa5BS

a7f65c93515a18…3c9e6e61e91dfe

3 in → 6 out12.0106 XPM657 B

AerL35yq…gE1jPnhy AYmXDTRZ…RjoLiimC AJiUWmxX…BMH9Vzvt AQe12e3Z…HeWcXVsQ AUoAjuAg…oYcX3CJZ

c520f99647d6c0…66045a955f9221

3 in → 6 out12.1737 XPM659 B

AerL35yq…gE1jPnhy AeqHkKVa…gMPwvJMM AYmXDTRZ…RjoLiimC AJiUWmxX…BMH9Vzvt AQe12e3Z…HeWcXVsQ

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.

1.224 × 10¹⁰¹(102-digit number)

12245895668630674355…37289194723660054079

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

1.224 × 10¹⁰¹(102-digit number)

12245895668630674355…37289194723660054079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.224 × 10¹⁰¹(102-digit number)

12245895668630674355…37289194723660054081

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

2.449 × 10¹⁰¹(102-digit number)

24491791337261348711…74578389447320108159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.449 × 10¹⁰¹(102-digit number)

24491791337261348711…74578389447320108161

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

4.898 × 10¹⁰¹(102-digit number)

48983582674522697423…49156778894640216319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.898 × 10¹⁰¹(102-digit number)

48983582674522697423…49156778894640216321

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

9.796 × 10¹⁰¹(102-digit number)

97967165349045394847…98313557789280432639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.796 × 10¹⁰¹(102-digit number)

97967165349045394847…98313557789280432641

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

1.959 × 10¹⁰²(103-digit number)

19593433069809078969…96627115578560865279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.959 × 10¹⁰²(103-digit number)

19593433069809078969…96627115578560865281

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