Block #342,179

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2014, 10:00:07 PM · Difficulty 10.1532 · 6,452,214 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77d4a3acfb963b4686ffd420c2d04f7a275acb4610eae00af3d274362dee0384

View on Chainz ↗

Height

#342,179

Difficulty

10.153215

Transactions

Size

1.84 KB

Version

Bits

0a273921

Nonce

36,890

Timestamp

1/3/2014, 10:00:07 PM

Confirmations

6,452,214

Mined by

⛏️ P2SHAQo5Sf84DcjUC65gbiaUvY1LDSCktZTnkR

Merkle Root

719523575441f9e19335221d26cae80daea4541ed09adc5b3a629e0263341118

Transactions (4)

Coinbasef642063350e90d…0d1cc231e4e58c

1 in → 1 out9.7300 XPM109 B

AQo5Sf84…CktZTnkR

41cc3dfd2e179b…cb6a4cf361af5a

1 in → 1 out9.7700 XPM158 B

AUQWNLX2…FxwsS5kV

a2f27a4fffa526…7be4a6fe4dbb66

6 in → 3 out15.0908 XPM1001 B

AZNbx9G8…6GNfpvoy AbpDNWqV…yQGH7THk ASHs3BR3…HuFA7Lpt

6f33f73eff83cf…8b1ce3ec187c1c

3 in → 2 out2.0119 XPM522 B

AZy9YnVf…3VpMNryH AbaNx7k2…XyDXJgqK

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.

2.741 × 10⁹⁷(98-digit number)

27411453578810520094…25210278625666012479

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

2.741 × 10⁹⁷(98-digit number)

27411453578810520094…25210278625666012479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.741 × 10⁹⁷(98-digit number)

27411453578810520094…25210278625666012481

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

5.482 × 10⁹⁷(98-digit number)

54822907157621040189…50420557251332024959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.482 × 10⁹⁷(98-digit number)

54822907157621040189…50420557251332024961

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

1.096 × 10⁹⁸(99-digit number)

10964581431524208037…00841114502664049919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.096 × 10⁹⁸(99-digit number)

10964581431524208037…00841114502664049921

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

2.192 × 10⁹⁸(99-digit number)

21929162863048416075…01682229005328099839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.192 × 10⁹⁸(99-digit number)

21929162863048416075…01682229005328099841

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

4.385 × 10⁹⁸(99-digit number)

43858325726096832151…03364458010656199679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.385 × 10⁹⁸(99-digit number)

43858325726096832151…03364458010656199681

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