Block #449,212

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/18/2014, 11:09:00 AM · Difficulty 10.3692 · 6,368,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

64d6516affaa8486be2dff3d0dcd047010ff8d57dca160672c01af7000ad6778

View on Chainz ↗

Height

#449,212

Difficulty

10.369244

Transactions

Size

395 B

Version

Bits

0a5e86cd

Nonce

193,429

Timestamp

3/18/2014, 11:09:00 AM

Confirmations

6,368,651

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f514476c7a0e91a52e8c7f621527bf21325d245bf97d8c21acbbdbf15f37fafa

Transactions (2)

Coinbase64369451f66908…793780b1aa8bea

1 in → 1 out9.3000 XPM110 B

AeKNrjNj…1NEq95Ta

cdf648bc3a063e…4d6eae49c8f310

1 in → 1 out9.3300 XPM192 B

AdTvQzvw…pbmp1pPd

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.

3.945 × 10¹⁰²(103-digit number)

39450508179902356462…63064765481468661759

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

3.945 × 10¹⁰²(103-digit number)

39450508179902356462…63064765481468661759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.945 × 10¹⁰²(103-digit number)

39450508179902356462…63064765481468661761

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

7.890 × 10¹⁰²(103-digit number)

78901016359804712925…26129530962937323519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.890 × 10¹⁰²(103-digit number)

78901016359804712925…26129530962937323521

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

1.578 × 10¹⁰³(104-digit number)

15780203271960942585…52259061925874647039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.578 × 10¹⁰³(104-digit number)

15780203271960942585…52259061925874647041

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

3.156 × 10¹⁰³(104-digit number)

31560406543921885170…04518123851749294079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.156 × 10¹⁰³(104-digit number)

31560406543921885170…04518123851749294081

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

6.312 × 10¹⁰³(104-digit number)

63120813087843770340…09036247703498588159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.312 × 10¹⁰³(104-digit number)

63120813087843770340…09036247703498588161

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 #449,212

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