Block #487,388

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 3:06:43 AM · Difficulty 10.6400 · 6,310,763 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ea9eb65fbdd5cdd6fdb71c250219c1a79427affece5305e550eaef83760b247

View on Chainz ↗

Height

#487,388

Difficulty

10.640007

Transactions

Size

434 B

Version

Bits

0aa3d782

Nonce

36,805,613

Timestamp

4/12/2014, 3:06:43 AM

Confirmations

6,310,763

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b67451ea547bb0214c9fab6b49f218bd83a3883d002212ce8f6e1598ee4e9ebc

Transactions (2)

Coinbaseef28e378458029…0837421f5fa129

1 in → 1 out8.8300 XPM116 B

AbwWkWZt…kawDhufa

39dc5dcb5252b7…2ff7d57aed6909

1 in → 2 out7.8718 XPM226 B

AVHJVjSQ…3xkh5k5p AXxp24rY…yi3yUFBu

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.

5.733 × 10⁹⁹(100-digit number)

57330713100781261596…16117696408759167999

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

5.733 × 10⁹⁹(100-digit number)

57330713100781261596…16117696408759167999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.733 × 10⁹⁹(100-digit number)

57330713100781261596…16117696408759168001

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

1.146 × 10¹⁰⁰(101-digit number)

11466142620156252319…32235392817518335999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.146 × 10¹⁰⁰(101-digit number)

11466142620156252319…32235392817518336001

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

2.293 × 10¹⁰⁰(101-digit number)

22932285240312504638…64470785635036671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.293 × 10¹⁰⁰(101-digit number)

22932285240312504638…64470785635036672001

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

4.586 × 10¹⁰⁰(101-digit number)

45864570480625009277…28941571270073343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.586 × 10¹⁰⁰(101-digit number)

45864570480625009277…28941571270073344001

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

9.172 × 10¹⁰⁰(101-digit number)

91729140961250018554…57883142540146687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.172 × 10¹⁰⁰(101-digit number)

91729140961250018554…57883142540146688001

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