Home/Chain Registry/Block #335,938

Block #335,938

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/30/2013, 2:47:06 PM · Difficulty 10.1433 · 6,465,457 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85ecf2f536c9ab0dbea6b637bf510da9bc5447c1d2e0b9323bb80ca2f9d499f0

View on Chainz ↗

Height

#335,938

Difficulty

10.143341

Transactions

Size

208 B

Version

Bits

0a24b1ff

Nonce

8,244

Timestamp

12/30/2013, 2:47:06 PM

Confirmations

6,465,457

Merkle Root

231e42ea3dffd41ba2b3e02c68f56ae66e25ec49af8bea20468b780feaa160b5

Transactions (1)

Coinbase231e42ea3dffd4…8b780feaa160b5

1 in → 1 out9.7000 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.

3.812 × 10¹⁰⁰(101-digit number)

38128913003301016884…10519528240834150400

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

3.812 × 10¹⁰⁰(101-digit number)

38128913003301016884…10519528240834150399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.812 × 10¹⁰⁰(101-digit number)

38128913003301016884…10519528240834150401

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

7.625 × 10¹⁰⁰(101-digit number)

76257826006602033769…21039056481668300799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.625 × 10¹⁰⁰(101-digit number)

76257826006602033769…21039056481668300801

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

1.525 × 10¹⁰¹(102-digit number)

15251565201320406753…42078112963336601599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.525 × 10¹⁰¹(102-digit number)

15251565201320406753…42078112963336601601

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

3.050 × 10¹⁰¹(102-digit number)

30503130402640813507…84156225926673203199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.050 × 10¹⁰¹(102-digit number)

30503130402640813507…84156225926673203201

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

6.100 × 10¹⁰¹(102-digit number)

61006260805281627015…68312451853346406399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.100 × 10¹⁰¹(102-digit number)

61006260805281627015…68312451853346406401

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 335938

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 85ecf2f536c9ab0dbea6b637bf510da9bc5447c1d2e0b9323bb80ca2f9d499f0

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #335,938 on Chainz ↗