Block #486,363

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 1:26:59 PM · Difficulty 10.6249 · 6,313,115 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3fa5a306fa29ef1896c116faaf0d2b2c96e89e3e68d0367298775bfa76771d6c

View on Chainz ↗

Height

#486,363

Difficulty

10.624931

Transactions

Size

1.23 KB

Version

Bits

0a9ffb72

Nonce

6,466,449

Timestamp

4/11/2014, 1:26:59 PM

Confirmations

6,313,115

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

68480b93b55bbb9cec00f4339e072d8b1c97c54b97274c8cbe53dfa485789954

Transactions (5)

Coinbasef75d15aee0f170…c91589c7fb5815

1 in → 1 out8.8800 XPM116 B

AbwWkWZt…kawDhufa

2f8464573394fb…7594d3eb5285e2

1 in → 2 out8.9500 XPM226 B

AdqH4QjD…3vhGVHG4 AbzERnKw…3xE1SYAE

bc084443c77b36…869ac3be8e8ef9

1 in → 2 out7.4263 XPM226 B

ANL6drQ6…UPF8uZX2 ALGHihes…5S3cTFuX

62e64a4b4d66a8…582738f0e4f8ee

1 in → 2 out5.8582 XPM226 B

AMU8nEj9…Eo32pqxr AXj2CPmt…aRht1Bed

a2547e37f53640…28fb715895ed07

2 in → 2 out2.1927 XPM375 B

ALciVp6Q…CVGfMuEt AVfAJAme…yw84suda

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.

2.424 × 10⁹⁷(98-digit number)

24245138873515912288…85939797447016202079

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

2.424 × 10⁹⁷(98-digit number)

24245138873515912288…85939797447016202079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.424 × 10⁹⁷(98-digit number)

24245138873515912288…85939797447016202081

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

4.849 × 10⁹⁷(98-digit number)

48490277747031824577…71879594894032404159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.849 × 10⁹⁷(98-digit number)

48490277747031824577…71879594894032404161

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

9.698 × 10⁹⁷(98-digit number)

96980555494063649155…43759189788064808319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.698 × 10⁹⁷(98-digit number)

96980555494063649155…43759189788064808321

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

1.939 × 10⁹⁸(99-digit number)

19396111098812729831…87518379576129616639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.939 × 10⁹⁸(99-digit number)

19396111098812729831…87518379576129616641

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

3.879 × 10⁹⁸(99-digit number)

38792222197625459662…75036759152259233279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.879 × 10⁹⁸(99-digit number)

38792222197625459662…75036759152259233281

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