Block #179,676

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/25/2013, 6:49:13 AM · Difficulty 9.8625 · 6,647,516 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23486f2cbd5415fd942066994ec924d6fc628671b8a8e2c8e0b9574b31d60df1

View on Chainz ↗

Height

#179,676

Difficulty

9.862548

Transactions

Size

652 B

Version

Bits

09dccff6

Nonce

70,573

Timestamp

9/25/2013, 6:49:13 AM

Confirmations

6,647,516

Mined by

⛏️ P2SHAHF9Qa57mG357Ti5HXSZogvHw9cw2T7NCS

Merkle Root

084839c7d40cd26540f27be8978147d7b6cd4a38ac68c5ecc8cc51d3c86b97d9

Transactions (3)

Coinbasefa84e8eb4d0c40…23e2516b55be2a

1 in → 1 out10.2900 XPM109 B

AHF9Qa57…cw2T7NCS

60bff956c484f2…1d78faa0ad9962

1 in → 2 out10.2500 XPM227 B

ANgghUhS…1dpbL8Pc AeXLk5Hy…anAHKAbj

f3d6ac27735846…baafbde0678821

1 in → 2 out10.2500 XPM226 B

AP4exjFF…2JJqgYei Ae4sZH4c…V3py9Cap

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.

3.860 × 10⁹⁵(96-digit number)

38605214893535473655…10652416769453260479

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

3.860 × 10⁹⁵(96-digit number)

38605214893535473655…10652416769453260479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.860 × 10⁹⁵(96-digit number)

38605214893535473655…10652416769453260481

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

7.721 × 10⁹⁵(96-digit number)

77210429787070947310…21304833538906520959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.721 × 10⁹⁵(96-digit number)

77210429787070947310…21304833538906520961

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

1.544 × 10⁹⁶(97-digit number)

15442085957414189462…42609667077813041919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.544 × 10⁹⁶(97-digit number)

15442085957414189462…42609667077813041921

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

3.088 × 10⁹⁶(97-digit number)

30884171914828378924…85219334155626083839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.088 × 10⁹⁶(97-digit number)

30884171914828378924…85219334155626083841

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

6.176 × 10⁹⁶(97-digit number)

61768343829656757848…70438668311252167679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #179,676

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