Block #338,662

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/1/2014, 3:24:41 PM · Difficulty 10.1219 · 6,457,626 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82cade4066adc7dded81d0c2ab019ff2717d6715600596eedcba2093d4de6030

View on Chainz ↗

Height

#338,662

Difficulty

10.121943

Transactions

Size

1.08 KB

Version

Bits

0a1f37a6

Nonce

6,847

Timestamp

1/1/2014, 3:24:41 PM

Confirmations

6,457,626

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

751ad5c2e41111df4d14449f098348867e885c41e4c00392fc06b8cf78cff591

Transactions (5)

Coinbase4c127925645915…b45e70574aa73f

1 in → 1 out9.7900 XPM110 B

AeKNrjNj…1NEq95Ta

7be6cc5a0325a1…2a89f265752e98

1 in → 2 out8.6259 XPM227 B

AckfnKMa…vhmiMsiq APKydzGq…WmaAeGxX

71520e7ecda913…f79876e374a341

1 in → 2 out6.6045 XPM225 B

AYkT7nDL…9fU1wXWa Ac8DQqUM…KHagDDrH

f09951697a65a2…744bc693f8547f

1 in → 2 out7.6067 XPM227 B

AGFyKJMC…UHLroc9B AGbhocGy…bBEp8MoY

61f2fb4d927b9c…db52dabde6ee3f

1 in → 2 out7.6025 XPM227 B

AL9CuC18…YRS58bQC AKmsnKFS…hETH9mC5

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.

2.124 × 10⁹⁹(100-digit number)

21246787401755460905…97093174290110499839

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

2.124 × 10⁹⁹(100-digit number)

21246787401755460905…97093174290110499839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.124 × 10⁹⁹(100-digit number)

21246787401755460905…97093174290110499841

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

4.249 × 10⁹⁹(100-digit number)

42493574803510921810…94186348580220999679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.249 × 10⁹⁹(100-digit number)

42493574803510921810…94186348580220999681

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

8.498 × 10⁹⁹(100-digit number)

84987149607021843620…88372697160441999359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.498 × 10⁹⁹(100-digit number)

84987149607021843620…88372697160441999361

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

1.699 × 10¹⁰⁰(101-digit number)

16997429921404368724…76745394320883998719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.699 × 10¹⁰⁰(101-digit number)

16997429921404368724…76745394320883998721

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

3.399 × 10¹⁰⁰(101-digit number)

33994859842808737448…53490788641767997439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.399 × 10¹⁰⁰(101-digit number)

33994859842808737448…53490788641767997441

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