Block #2,418,193

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2017, 9:05:58 PM · Difficulty 10.9051 · 4,424,636 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce11a27e7a503aa14ed3d98f7dfac01459c5e2b7ab385d11daa2ceb944a12138

View on Chainz ↗

Height

#2,418,193

Difficulty

10.905117

Transactions

Size

1.05 KB

Version

Bits

0ae7b5c5

Nonce

833,120,909

Timestamp

12/10/2017, 9:05:58 PM

Confirmations

4,424,636

Mined by

⛏️ P2SHAY1dCxyHC2DanBzEyunhLjsVhyfrYdYmfQ

Merkle Root

bb3a8e2f19ed293d07918cad0e9c2ee5a4a44085e99043cbb3bc6b6276d2c21b

Transactions (3)

Coinbased5802dedd62c3b…0ea16e81a4c515

1 in → 1 out8.4200 XPM110 B

AY1dCxyH…frYdYmfQ

bc17ab8098aa5b…2ee03fa4e1d6ec

1 in → 10 out39.8800 XPM498 B

AbDTiZkp…h3urwjt9 AFu9UEEM…R991pCL2 AG3b7KoX…BMDS1p7k AcpVc45Q…JGLJnd6X Ab2LENg7…m8MPQHhy

c6d0ae9a135605…39eb521750dc72

2 in → 2 out4.9313 XPM374 B

AY5AjcNG…6UC73suK AMjZ87GH…cvurqAXE

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.

5.024 × 10⁹⁴(95-digit number)

50246055798673146578…04360886771174828799

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

5.024 × 10⁹⁴(95-digit number)

50246055798673146578…04360886771174828799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.024 × 10⁹⁴(95-digit number)

50246055798673146578…04360886771174828801

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

1.004 × 10⁹⁵(96-digit number)

10049211159734629315…08721773542349657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.004 × 10⁹⁵(96-digit number)

10049211159734629315…08721773542349657601

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

2.009 × 10⁹⁵(96-digit number)

20098422319469258631…17443547084699315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.009 × 10⁹⁵(96-digit number)

20098422319469258631…17443547084699315201

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

4.019 × 10⁹⁵(96-digit number)

40196844638938517263…34887094169398630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.019 × 10⁹⁵(96-digit number)

40196844638938517263…34887094169398630401

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

8.039 × 10⁹⁵(96-digit number)

80393689277877034526…69774188338797260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.039 × 10⁹⁵(96-digit number)

80393689277877034526…69774188338797260801

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 #2,418,193

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