Block #2,478,983

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2018, 3:36:11 PM · Difficulty 10.9657 · 4,354,351 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ce18ec44f013f3dfd37e2a623cbcff386905e8a5ad66bb72cb000010cb404c4

View on Chainz ↗

Height

#2,478,983

Difficulty

10.965717

Transactions

Size

6.78 KB

Version

Bits

0af7393e

Nonce

222,366,518

Timestamp

1/18/2018, 3:36:11 PM

Confirmations

4,354,351

Mined by

⛏️ P2SHAGA8HtAVvEusmXTt92NCiTjL3NSVhKEjXK

Merkle Root

cf742cb174d0378710fe276fccaffb1ca7b76f65755ea1766fc7089991e41054

Transactions (2)

Coinbase8819e0b56c621d…dea48697c406b2

1 in → 1 out8.3700 XPM110 B

AGA8HtAV…SVhKEjXK

d4c8aa33fe1dd0…df645f6c8a7b81

45 in → 2 out4726.2925 XPM6.58 KB

AR1e7roQ…hFWtfkam AMRycWoF…13hkF5ou

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.

7.700 × 10⁹⁸(99-digit number)

77007624668028849289…14776127799466393599

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

7.700 × 10⁹⁸(99-digit number)

77007624668028849289…14776127799466393599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.700 × 10⁹⁸(99-digit number)

77007624668028849289…14776127799466393601

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

1.540 × 10⁹⁹(100-digit number)

15401524933605769857…29552255598932787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.540 × 10⁹⁹(100-digit number)

15401524933605769857…29552255598932787201

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

3.080 × 10⁹⁹(100-digit number)

30803049867211539715…59104511197865574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.080 × 10⁹⁹(100-digit number)

30803049867211539715…59104511197865574401

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

6.160 × 10⁹⁹(100-digit number)

61606099734423079431…18209022395731148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.160 × 10⁹⁹(100-digit number)

61606099734423079431…18209022395731148801

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

1.232 × 10¹⁰⁰(101-digit number)

12321219946884615886…36418044791462297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.232 × 10¹⁰⁰(101-digit number)

12321219946884615886…36418044791462297601

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 #2,478,983

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