Block #361,792

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/16/2014, 7:28:28 AM · Difficulty 10.4083 · 6,437,124 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1e9cc64f2f3ef41ec6e99401fe387042ff230ebad837fd2701dabb407498bac5

View on Chainz ↗

Height

#361,792

Difficulty

10.408303

Transactions

Size

1.01 KB

Version

Bits

0a688686

Nonce

1,278

Timestamp

1/16/2014, 7:28:28 AM

Confirmations

6,437,124

Mined by

⛏️ @aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6ddbe6d1badf542e9e764afe6c28593d7bb4f514e9b521988e63555f0225c0e5

Transactions (1)

Coinbase6ddbe6d1badf54…63555f0225c0e5

1 in → 26 out9.2200 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AQwRN8bE…V8PsTcY9 AKzkYQaQ…zR4FspJZ

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.

8.988 × 10⁹⁹(100-digit number)

89886645617306480823…30746700657971162879

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

8.988 × 10⁹⁹(100-digit number)

89886645617306480823…30746700657971162879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.988 × 10⁹⁹(100-digit number)

89886645617306480823…30746700657971162881

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

1.797 × 10¹⁰⁰(101-digit number)

17977329123461296164…61493401315942325759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.797 × 10¹⁰⁰(101-digit number)

17977329123461296164…61493401315942325761

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

3.595 × 10¹⁰⁰(101-digit number)

35954658246922592329…22986802631884651519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.595 × 10¹⁰⁰(101-digit number)

35954658246922592329…22986802631884651521

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

7.190 × 10¹⁰⁰(101-digit number)

71909316493845184658…45973605263769303039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.190 × 10¹⁰⁰(101-digit number)

71909316493845184658…45973605263769303041

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

1.438 × 10¹⁰¹(102-digit number)

14381863298769036931…91947210527538606079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.438 × 10¹⁰¹(102-digit number)

14381863298769036931…91947210527538606081

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