Block #177,387

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/23/2013, 3:34:32 PM · Difficulty 9.8642 · 6,614,473 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

da18ce3d7db178e3e2b352bda94eb6bade47a9a3385f3a02442ecbcfd32ae59b

View on Chainz ↗

Height

#177,387

Difficulty

9.864219

Transactions

Size

198 B

Version

Bits

09dd3d7c

Nonce

69,677

Timestamp

9/23/2013, 3:34:32 PM

Confirmations

6,614,473

Merkle Root

998d44772230c7beb5733d4f52dcf680b64eadfa0798b786fbeb3ab73358e80b

Transactions (1)

Coinbase998d44772230c7…eb3ab73358e80b

1 in → 1 out10.2600 XPM109 B

Af4wD75X…Lxgjq8Ud

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.

1.673 × 10⁹³(94-digit number)

16734587616519459895…60894823957755833599

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

1.673 × 10⁹³(94-digit number)

16734587616519459895…60894823957755833599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.673 × 10⁹³(94-digit number)

16734587616519459895…60894823957755833601

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

3.346 × 10⁹³(94-digit number)

33469175233038919791…21789647915511667199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.346 × 10⁹³(94-digit number)

33469175233038919791…21789647915511667201

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

6.693 × 10⁹³(94-digit number)

66938350466077839582…43579295831023334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.693 × 10⁹³(94-digit number)

66938350466077839582…43579295831023334401

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

1.338 × 10⁹⁴(95-digit number)

13387670093215567916…87158591662046668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.338 × 10⁹⁴(95-digit number)

13387670093215567916…87158591662046668801

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

2.677 × 10⁹⁴(95-digit number)

26775340186431135833…74317183324093337599

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