Block #358,171

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 9:30:53 PM · Difficulty 10.3905 · 6,441,412 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef9b8424e2de27a8ab573ddf832b476b54bc9cd3badcec7063059fb75801c406

View on Chainz ↗

Height

#358,171

Difficulty

10.390477

Transactions

Size

1.22 KB

Version

Bits

0a63f64f

Nonce

314,683

Timestamp

1/13/2014, 9:30:53 PM

Confirmations

6,441,412

Mined by

⛏️ P2SHAVM1afAzTfcVPUXn9oTQzchAG6bstSGvq8

Merkle Root

1437ac4756e0d13b62aefbe5372604a1706a343a24e607a13862951f1feb82df

Transactions (5)

Coinbase4cf245091551dc…2466f95554f4be

1 in → 1 out9.2900 XPM109 B

AVM1afAz…bstSGvq8

f010193f223c5a…aadc7cb17a5b6f

1 in → 2 out5.2633 XPM225 B

AHDMXuc2…qvJiSGGU ANWwHf2k…qgjhEZxi

995cfeda1ffdea…95259cc389adb4

1 in → 2 out3.6512 XPM225 B

AGUiHrXX…99nzH74G ASUwAU5F…PLuaSjtb

81fd8d1daf93f8…853c5bc8edba7c

1 in → 2 out4.2696 XPM226 B

AYVyegUo…88drMYWV AZqpr5iC…UVZD1knQ

8b584cf4b2dda0…15ae589a697f02

2 in → 2 out1.6886 XPM375 B

AUY8KZt9…Wr5f3A71 ALWY1Aqp…wGPyvzdF

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.

4.534 × 10⁹⁹(100-digit number)

45343435120152274037…46427689548511174409

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

4.534 × 10⁹⁹(100-digit number)

45343435120152274037…46427689548511174409

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.534 × 10⁹⁹(100-digit number)

45343435120152274037…46427689548511174411

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

9.068 × 10⁹⁹(100-digit number)

90686870240304548075…92855379097022348819

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.068 × 10⁹⁹(100-digit number)

90686870240304548075…92855379097022348821

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

1.813 × 10¹⁰⁰(101-digit number)

18137374048060909615…85710758194044697639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.813 × 10¹⁰⁰(101-digit number)

18137374048060909615…85710758194044697641

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

3.627 × 10¹⁰⁰(101-digit number)

36274748096121819230…71421516388089395279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.627 × 10¹⁰⁰(101-digit number)

36274748096121819230…71421516388089395281

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

7.254 × 10¹⁰⁰(101-digit number)

72549496192243638460…42843032776178790559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.254 × 10¹⁰⁰(101-digit number)

72549496192243638460…42843032776178790561

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