Block #358,302

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/14/2014, 12:02:29 AM · Difficulty 10.3879 · 6,437,983 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4bb9ddcc0756c07ad88ccf0dfda6a5e00c7dac3576aad403839d150dd866046

View on Chainz ↗

Height

#358,302

Difficulty

10.387873

Transactions

Size

725 B

Version

Bits

0a634baa

Nonce

114,984

Timestamp

1/14/2014, 12:02:29 AM

Confirmations

6,437,983

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ef0b2b9b4677c47e4b215f5f4fdddbc0045d5d0782730360ae497fc5a255b97e

Transactions (2)

Coinbase9be10efd2b4b55…0a537ace9ecaab

1 in → 1 out9.2600 XPM110 B

AeKNrjNj…1NEq95Ta

6f23c8461dae3d…67422a6d21b0ea

3 in → 2 out48.7200 XPM524 B

ASbnd1dV…EFMF9knR AZHEpaqf…MxbjTDc5

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.

4.486 × 10⁹⁷(98-digit number)

44868729542139339677…10642808792269548179

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

4.486 × 10⁹⁷(98-digit number)

44868729542139339677…10642808792269548179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.486 × 10⁹⁷(98-digit number)

44868729542139339677…10642808792269548181

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

8.973 × 10⁹⁷(98-digit number)

89737459084278679354…21285617584539096359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.973 × 10⁹⁷(98-digit number)

89737459084278679354…21285617584539096361

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

1.794 × 10⁹⁸(99-digit number)

17947491816855735870…42571235169078192719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.794 × 10⁹⁸(99-digit number)

17947491816855735870…42571235169078192721

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

3.589 × 10⁹⁸(99-digit number)

35894983633711471741…85142470338156385439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.589 × 10⁹⁸(99-digit number)

35894983633711471741…85142470338156385441

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

7.178 × 10⁹⁸(99-digit number)

71789967267422943483…70284940676312770879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.178 × 10⁹⁸(99-digit number)

71789967267422943483…70284940676312770881

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