Block #447,817

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 12:36:51 PM · Difficulty 10.3623 · 6,357,927 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bdab4195f1c5cda9afab7e2e82dcd2a410cab5f671804a35cae7aa39f79fd1b

View on Chainz ↗

Height

#447,817

Difficulty

10.362334

Transactions

Size

895 B

Version

Bits

0a5cc1f3

Nonce

45,535

Timestamp

3/17/2014, 12:36:51 PM

Confirmations

6,357,927

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

bbabe0f86ddea7be81164c5b56b01eb0ca19df96c99bd6c43b2d02cf054c0480

Transactions (2)

Coinbaseb30d16c296327e…ff6639666f5db7

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

61e5ba812c8b3a…0af14bbbde65f4

3 in → 10 out28.0100 XPM692 B

AXhMhCgP…4HpqiDxJ AQ1R6V2e…Ch7Bdubb AeKNrjNj…1NEq95Ta ARobqFaw…sqUDMdNr ANAuMTQp…5p9EL5ao

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.

1.390 × 10¹⁰¹(102-digit number)

13909630385052815524…20671702282661439519

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

1.390 × 10¹⁰¹(102-digit number)

13909630385052815524…20671702282661439519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.390 × 10¹⁰¹(102-digit number)

13909630385052815524…20671702282661439521

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

2.781 × 10¹⁰¹(102-digit number)

27819260770105631048…41343404565322879039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.781 × 10¹⁰¹(102-digit number)

27819260770105631048…41343404565322879041

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

5.563 × 10¹⁰¹(102-digit number)

55638521540211262096…82686809130645758079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.563 × 10¹⁰¹(102-digit number)

55638521540211262096…82686809130645758081

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

1.112 × 10¹⁰²(103-digit number)

11127704308042252419…65373618261291516159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.112 × 10¹⁰²(103-digit number)

11127704308042252419…65373618261291516161

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

2.225 × 10¹⁰²(103-digit number)

22255408616084504838…30747236522583032319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.225 × 10¹⁰²(103-digit number)

22255408616084504838…30747236522583032321

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