Block #177,351

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/23/2013, 2:57:43 PM · Difficulty 9.8642 · 6,632,225 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a390889d88cc096157fe117897126cdc9a9f61e8386db268a1a219ae755fc8a0

View on Chainz ↗

Height

#177,351

Difficulty

9.864227

Transactions

Size

1.35 KB

Version

Bits

09dd3df7

Nonce

19,010

Timestamp

9/23/2013, 2:57:43 PM

Confirmations

6,632,225

Mined by

⛏️ P2SHAZXR2VqnboMnmeLSgtbXPE9oCu1sWGjL6t

Merkle Root

0a9a762c3f541454b3a878948c06b8c9d540c054806355d8e0855dc959e9c8fd

Transactions (3)

Coinbasef1ab9a57878eb1…f88c9169152fde

1 in → 1 out10.2800 XPM109 B

AZXR2Vqn…1sWGjL6t

cd3a3fc5743847…2577106fa76147

8 in → 1 out82.8300 XPM955 B

AJmQUgPF…Lzi626sb

29cdde2040e5ac…0d3a458730ab52

1 in → 2 out0.3110 XPM227 B

ALRpbUZP…DAy99T2X AW1o6TBj…KP6hSLnx

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.

1.721 × 10⁹²(93-digit number)

17214646461419560680…21426023007921574119

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

1.721 × 10⁹²(93-digit number)

17214646461419560680…21426023007921574119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.721 × 10⁹²(93-digit number)

17214646461419560680…21426023007921574121

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

3.442 × 10⁹²(93-digit number)

34429292922839121361…42852046015843148239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.442 × 10⁹²(93-digit number)

34429292922839121361…42852046015843148241

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

6.885 × 10⁹²(93-digit number)

68858585845678242723…85704092031686296479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.885 × 10⁹²(93-digit number)

68858585845678242723…85704092031686296481

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

1.377 × 10⁹³(94-digit number)

13771717169135648544…71408184063372592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.377 × 10⁹³(94-digit number)

13771717169135648544…71408184063372592961

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

2.754 × 10⁹³(94-digit number)

27543434338271297089…42816368126745185919

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 #177,351

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