Block #246,906

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 10:58:12 AM · Difficulty 9.9644 · 6,563,659 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f86a3fe3ca73b021a7b802798e8984b97468d32d1c1c0eedf2f0030c30bc366b

View on Chainz ↗

Height

#246,906

Difficulty

9.964365

Transactions

Size

2.01 KB

Version

Bits

09f6e09d

Nonce

8,582

Timestamp

11/6/2013, 10:58:12 AM

Confirmations

6,563,659

Mined by

⛏️ zRzAcEnwywzxWFA99sBpHvfDrnmMpvZtt2xTs

Merkle Root

184f66c143d364443c1fa89abe87d674b92827c95275a0e790b54b505979dd87

Transactions (1)

Coinbase184f66c143d364…b54b505979dd87

1 in → 56 out10.0400 XPM1.92 KB

AcEnwywz…vZtt2xTs ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk ARR7aRH6…ne3DXGXZ ALzxhR4e…bD4bNcZe

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.

3.757 × 10⁹³(94-digit number)

37577589830007060602…41361784113816326769

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

3.757 × 10⁹³(94-digit number)

37577589830007060602…41361784113816326769

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.757 × 10⁹³(94-digit number)

37577589830007060602…41361784113816326771

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

7.515 × 10⁹³(94-digit number)

75155179660014121205…82723568227632653539

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.515 × 10⁹³(94-digit number)

75155179660014121205…82723568227632653541

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

1.503 × 10⁹⁴(95-digit number)

15031035932002824241…65447136455265307079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.503 × 10⁹⁴(95-digit number)

15031035932002824241…65447136455265307081

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

3.006 × 10⁹⁴(95-digit number)

30062071864005648482…30894272910530614159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.006 × 10⁹⁴(95-digit number)

30062071864005648482…30894272910530614161

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

6.012 × 10⁹⁴(95-digit number)

60124143728011296964…61788545821061228319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.012 × 10⁹⁴(95-digit number)

60124143728011296964…61788545821061228321

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 #246,906

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