Block #336,540

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 1:01:26 AM · Difficulty 10.1414 · 6,473,060 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8aee2da1e079e79f8f9e8e398992c2e20e8992e10f72295cc7b5b1033744270

View on Chainz ↗

Height

#336,540

Difficulty

10.141361

Transactions

Size

1.45 KB

Version

Bits

0a243042

Nonce

177,374

Timestamp

12/31/2013, 1:01:26 AM

Confirmations

6,473,060

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

75c3bf9f3c56324ef2e629e57f0055b7e8e852f634a6447fe57930f0ca7c53e4

Transactions (5)

Coinbase25814945cb90c2…120498d8fc7cbf

1 in → 1 out9.7500 XPM110 B

AeKNrjNj…1NEq95Ta

d72b3e247eca88…52f47529e5d5e5

2 in → 2 out37.8900 XPM375 B

ALU8V6xp…qYyzJHPe AGUbpYQA…PgUVXGfZ

7628ae86b30bc2…41479823ac17a5

1 in → 1 out9.6700 XPM158 B

AJaoEgRb…eZTiDYf2

8a4fc32f641c5e…f516369bdc1b77

1 in → 2 out2157.1428 XPM225 B

AZqUM83N…c2pU4Jx7 AVGU2bzd…rthpEc12

4d0f11cb01c3e1…e3fe1314f9c63d

3 in → 2 out0.4500 XPM522 B

AKFuBr2K…ELKWRLmy AJGywhHS…zeWRnoVL

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.

9.138 × 10⁹⁷(98-digit number)

91381608487478444169…74667135909176114399

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

9.138 × 10⁹⁷(98-digit number)

91381608487478444169…74667135909176114399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.138 × 10⁹⁷(98-digit number)

91381608487478444169…74667135909176114401

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

1.827 × 10⁹⁸(99-digit number)

18276321697495688833…49334271818352228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.827 × 10⁹⁸(99-digit number)

18276321697495688833…49334271818352228801

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

3.655 × 10⁹⁸(99-digit number)

36552643394991377667…98668543636704457599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.655 × 10⁹⁸(99-digit number)

36552643394991377667…98668543636704457601

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

7.310 × 10⁹⁸(99-digit number)

73105286789982755335…97337087273408915199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.310 × 10⁹⁸(99-digit number)

73105286789982755335…97337087273408915201

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

1.462 × 10⁹⁹(100-digit number)

14621057357996551067…94674174546817830399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.462 × 10⁹⁹(100-digit number)

14621057357996551067…94674174546817830401

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 #336,540

Cookie Preferences