Block #393,004

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 7:57:02 PM · Difficulty 10.4441 · 6,413,059 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9caccb0538009d791e2f1c8a3fc1c6bb220b866d9721e372310ec927a54989f3

View on Chainz ↗

Height

#393,004

Difficulty

10.444077

Transactions

Size

1.42 KB

Version

Bits

0a71af08

Nonce

410,063

Timestamp

2/6/2014, 7:57:02 PM

Confirmations

6,413,059

Mined by

⛏️ ,2WAcs9SHrkBk52E7r7T3v7yemDoFQJSB8SFG

Merkle Root

b32ceebf9fbfa62ee8b4e3ce73e2d2761b2ec46df02cf4f6f7d9d0ad99d51df2

Transactions (2)

Coinbase5b79e293234be6…b4eee4589f90f3

1 in → 19 out9.1600 XPM709 B

Acs9SHrk…QJSB8SFG AW2fas42…gGAHYdHj AUzEPJFG…kYkA5U9V AbPcCMg4…719q6mAX ATLD7BNP…nPjXCb2h

8698b250fb6cac…8d95f14b5c9da8

3 in → 8 out21.6518 XPM659 B

ANZssFj6…3NCAQScE AeKNrjNj…1NEq95Ta AT8akpZ5…X48Kza4D AZZ9mXy8…bVJfUD26 AJtMDaUx…bUaiUT9g

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.

3.550 × 10⁹⁶(97-digit number)

35503198773801211234…36056782035286744639

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

3.550 × 10⁹⁶(97-digit number)

35503198773801211234…36056782035286744639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.550 × 10⁹⁶(97-digit number)

35503198773801211234…36056782035286744641

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

7.100 × 10⁹⁶(97-digit number)

71006397547602422469…72113564070573489279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.100 × 10⁹⁶(97-digit number)

71006397547602422469…72113564070573489281

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

1.420 × 10⁹⁷(98-digit number)

14201279509520484493…44227128141146978559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.420 × 10⁹⁷(98-digit number)

14201279509520484493…44227128141146978561

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

2.840 × 10⁹⁷(98-digit number)

28402559019040968987…88454256282293957119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.840 × 10⁹⁷(98-digit number)

28402559019040968987…88454256282293957121

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

5.680 × 10⁹⁷(98-digit number)

56805118038081937975…76908512564587914239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.680 × 10⁹⁷(98-digit number)

56805118038081937975…76908512564587914241

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