Block #449,242

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/18/2014, 11:25:45 AM · Difficulty 10.3702 · 6,348,910 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16a0d2697622eaa8e467db259142bc916db3f984d8e5f582458cd92ac6652a39

View on Chainz ↗

Height

#449,242

Difficulty

10.370211

Transactions

Size

896 B

Version

Bits

0a5ec62d

Nonce

230,494

Timestamp

3/18/2014, 11:25:45 AM

Confirmations

6,348,910

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

129d1c68a6b0db87f86acb33ba9a36cac16e7aaa5ff1b00334793cb110a839cf

Transactions (2)

Coinbasecd45ad9dfe06a8…1b274f5e18eeb3

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

7526154b762615…d21446dd078550

3 in → 10 out27.9400 XPM694 B

AeKNrjNj…1NEq95Ta AZ9Gm8Uz…fgcHofTo AKQWmcgr…19EWDnMq AYTRzzG8…Wy9rUwgM AZZSguRi…GvQsves1

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.

6.074 × 10⁹⁹(100-digit number)

60748313503490209605…93008092122894687189

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

6.074 × 10⁹⁹(100-digit number)

60748313503490209605…93008092122894687189

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.074 × 10⁹⁹(100-digit number)

60748313503490209605…93008092122894687191

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

1.214 × 10¹⁰⁰(101-digit number)

12149662700698041921…86016184245789374379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.214 × 10¹⁰⁰(101-digit number)

12149662700698041921…86016184245789374381

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

2.429 × 10¹⁰⁰(101-digit number)

24299325401396083842…72032368491578748759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.429 × 10¹⁰⁰(101-digit number)

24299325401396083842…72032368491578748761

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

4.859 × 10¹⁰⁰(101-digit number)

48598650802792167684…44064736983157497519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.859 × 10¹⁰⁰(101-digit number)

48598650802792167684…44064736983157497521

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

9.719 × 10¹⁰⁰(101-digit number)

97197301605584335368…88129473966314995039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.719 × 10¹⁰⁰(101-digit number)

97197301605584335368…88129473966314995041

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