Home/Chain Registry/Block #334,138

Block #334,138

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 7:15:17 AM · Difficulty 10.1579 · 6,461,452 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de4b50dc4ebcd7d752b9cb1a6d0b3455aa1afcebc3b534d47c52c57120060094

View on Chainz ↗

Height

#334,138

Difficulty

10.157876

Transactions

Size

209 B

Version

Bits

0a286a96

Nonce

1,298

Timestamp

12/29/2013, 7:15:17 AM

Confirmations

6,461,452

Merkle Root

7d25a5852c0c21ac10dbd6e73d98660c9f3fc5a828497259a3c7b4a35a448fa4

Transactions (1)

Coinbase7d25a5852c0c21…c7b4a35a448fa4

1 in → 1 out9.6800 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.

9.384 × 10¹⁰⁰(101-digit number)

93846857596409916504…65923207109554503680

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

9.384 × 10¹⁰⁰(101-digit number)

93846857596409916504…65923207109554503679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.384 × 10¹⁰⁰(101-digit number)

93846857596409916504…65923207109554503681

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

1.876 × 10¹⁰¹(102-digit number)

18769371519281983300…31846414219109007359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.876 × 10¹⁰¹(102-digit number)

18769371519281983300…31846414219109007361

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

3.753 × 10¹⁰¹(102-digit number)

37538743038563966601…63692828438218014719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.753 × 10¹⁰¹(102-digit number)

37538743038563966601…63692828438218014721

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

7.507 × 10¹⁰¹(102-digit number)

75077486077127933203…27385656876436029439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.507 × 10¹⁰¹(102-digit number)

75077486077127933203…27385656876436029441

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

1.501 × 10¹⁰²(103-digit number)

15015497215425586640…54771313752872058879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.501 × 10¹⁰²(103-digit number)

15015497215425586640…54771313752872058881

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 334138

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 de4b50dc4ebcd7d752b9cb1a6d0b3455aa1afcebc3b534d47c52c57120060094

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 #334,138 on Chainz ↗