Block #329,084

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 5:31:01 PM · Difficulty 10.1708 · 6,487,458 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8dd156a56efbbc80ea9e721b60daa2422cd3efee498ca766628bdee3112e9a89

View on Chainz ↗

Height

#329,084

Difficulty

10.170778

Transactions

Size

205 B

Version

Bits

0a2bb817

Nonce

29,693

Timestamp

12/25/2013, 5:31:01 PM

Confirmations

6,487,458

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c489affb58347b266b6fda2106d6c3afbba306330751334075e12217a37cd3db

Transactions (1)

Coinbasec489affb58347b…e12217a37cd3db

1 in → 1 out9.6500 XPM116 B

AbwWkWZt…kawDhufa

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.

5.795 × 10⁹¹(92-digit number)

57951763683278765748…96647287759518191999

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

5.795 × 10⁹¹(92-digit number)

57951763683278765748…96647287759518191999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.795 × 10⁹¹(92-digit number)

57951763683278765748…96647287759518192001

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

1.159 × 10⁹²(93-digit number)

11590352736655753149…93294575519036383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.159 × 10⁹²(93-digit number)

11590352736655753149…93294575519036384001

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

2.318 × 10⁹²(93-digit number)

23180705473311506299…86589151038072767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.318 × 10⁹²(93-digit number)

23180705473311506299…86589151038072768001

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

4.636 × 10⁹²(93-digit number)

46361410946623012599…73178302076145535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.636 × 10⁹²(93-digit number)

46361410946623012599…73178302076145536001

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

9.272 × 10⁹²(93-digit number)

92722821893246025198…46356604152291071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.272 × 10⁹²(93-digit number)

92722821893246025198…46356604152291072001

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 #329,084

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