Block #488,658

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 8:03:00 PM · Difficulty 10.6581 · 6,306,861 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d82bfe12484c4c12bfc3fb2fee9999c9474770dfa4a0943ad0b2ad99bc0d849

View on Chainz ↗

Height

#488,658

Difficulty

10.658123

Transactions

Size

2.96 KB

Version

Bits

0aa87abd

Nonce

46,326,708

Timestamp

4/12/2014, 8:03:00 PM

Confirmations

6,306,861

Mined by

⛏️ P2SHATHfA9jzx3zHMbnefQ7DZd7TYNZAXaDNyh

Merkle Root

21b00902717033cc7c671d8a333ead7082a93394ef06243dd3ad2a7779f1d5df

Transactions (5)

Coinbase325448e9c80611…b193213aeda913

1 in → 1 out8.8500 XPM110 B

ATHfA9jz…ZAXaDNyh

dfff0e50de8937…dac9c0781fa41c

12 in → 2 out15.0101 XPM1.81 KB

AMeLP7im…kjdGrNnM AYBcWqRD…4hX8zZ9M

77c89fd3bc010b…f1b2aa39044b91

1 in → 2 out5.6858 XPM227 B

AceSi4nc…MdXFen4r ANAkFa7h…Qnby3Xgg

cd2bf371935d72…1af9b7ba02ac07

1 in → 2 out5.8210 XPM227 B

APbdJaha…FnDNQ5yE AaoacwLQ…MCVEcKii

080da5e4ea34eb…864c8ce854f23a

3 in → 2 out5.1005 XPM523 B

AenGiSGP…VmaExxbt AHRFBC52…Sxt2Nt8i

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.

1.375 × 10⁹⁶(97-digit number)

13758757690076283157…54728874779279591679

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

1.375 × 10⁹⁶(97-digit number)

13758757690076283157…54728874779279591679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.375 × 10⁹⁶(97-digit number)

13758757690076283157…54728874779279591681

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

2.751 × 10⁹⁶(97-digit number)

27517515380152566314…09457749558559183359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.751 × 10⁹⁶(97-digit number)

27517515380152566314…09457749558559183361

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

5.503 × 10⁹⁶(97-digit number)

55035030760305132628…18915499117118366719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.503 × 10⁹⁶(97-digit number)

55035030760305132628…18915499117118366721

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

1.100 × 10⁹⁷(98-digit number)

11007006152061026525…37830998234236733439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.100 × 10⁹⁷(98-digit number)

11007006152061026525…37830998234236733441

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

2.201 × 10⁹⁷(98-digit number)

22014012304122053051…75661996468473466879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.201 × 10⁹⁷(98-digit number)

22014012304122053051…75661996468473466881

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