Block #490,751

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 1:41:40 AM · Difficulty 10.6789 · 6,322,225 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83ee94f0c678eff9dcc166c345ecf7a080e365979b1bdf1789a10fdeee2a5109

View on Chainz ↗

Height

#490,751

Difficulty

10.678929

Transactions

Size

1.95 KB

Version

Bits

0aadce49

Nonce

5,625

Timestamp

4/14/2014, 1:41:40 AM

Confirmations

6,322,225

Mined by

⛏️ P2SHARcH5f9c8P5dLYuu8XJuFvaZuqyhfMysa5

Merkle Root

5ecc04e269d4511c7ddb69ae439339be37cd686df4ea123c78dac047edddcc60

Transactions (5)

Coinbase613a0abc1dc90d…0630c33ff17a43

1 in → 1 out8.8000 XPM111 B

ARcH5f9c…yhfMysa5

ed23ad343fe83c…e2974ff343cc8f

4 in → 2 out36.3500 XPM671 B

AGe4pJoK…LvQFc4DW AY3pJeNv…uDU6Lc1y

c8a802880426f5…9a225b7b242361

1 in → 2 out8.8100 XPM227 B

AaBAYKij…vPs6UjJZ APCza2xF…NYW1bK7F

9d9f503c50b0d8…e60ae18507944a

1 in → 2 out8.8100 XPM225 B

AYR6iBPP…nGvydeAB AKKoMa7P…tofb1RZy

db61e0b671ce63…a01191da5b1cad

4 in → 2 out5.1309 XPM672 B

AVDyPuA9…b4PxSrce AQxuAjby…xt1RWP1v

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.

2.682 × 10⁹⁸(99-digit number)

26827741623362100858…16456195897319349119

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

2.682 × 10⁹⁸(99-digit number)

26827741623362100858…16456195897319349119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.682 × 10⁹⁸(99-digit number)

26827741623362100858…16456195897319349121

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

5.365 × 10⁹⁸(99-digit number)

53655483246724201716…32912391794638698239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.365 × 10⁹⁸(99-digit number)

53655483246724201716…32912391794638698241

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

1.073 × 10⁹⁹(100-digit number)

10731096649344840343…65824783589277396479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.073 × 10⁹⁹(100-digit number)

10731096649344840343…65824783589277396481

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

2.146 × 10⁹⁹(100-digit number)

21462193298689680686…31649567178554792959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.146 × 10⁹⁹(100-digit number)

21462193298689680686…31649567178554792961

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

4.292 × 10⁹⁹(100-digit number)

42924386597379361373…63299134357109585919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.292 × 10⁹⁹(100-digit number)

42924386597379361373…63299134357109585921

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 #490,751

Cookie Preferences