Home/Chain Registry/Block #345,827

Block #345,827

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 4:37:05 AM · Difficulty 10.2143 · 6,445,826 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eba61eb82bce24aaa8c14e561dda5511a6ff365d8b16173cde252c2aba4ecb42

View on Chainz ↗

Height

#345,827

Difficulty

10.214330

Transactions

Size

209 B

Version

Bits

0a36de56

Nonce

1,664

Timestamp

1/6/2014, 4:37:05 AM

Confirmations

6,445,826

Merkle Root

ce9bcbf877aa1256d71347d9fd97d8d8d60a1234abb767c292cbb1b21791cd93

Transactions (1)

Coinbasece9bcbf877aa12…cbb1b21791cd93

1 in → 1 out9.5700 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.

8.882 × 10¹⁰⁰(101-digit number)

88826017461078206844…70320433274904483840

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

8.882 × 10¹⁰⁰(101-digit number)

88826017461078206844…70320433274904483839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.882 × 10¹⁰⁰(101-digit number)

88826017461078206844…70320433274904483841

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

1.776 × 10¹⁰¹(102-digit number)

17765203492215641368…40640866549808967679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.776 × 10¹⁰¹(102-digit number)

17765203492215641368…40640866549808967681

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

3.553 × 10¹⁰¹(102-digit number)

35530406984431282737…81281733099617935359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.553 × 10¹⁰¹(102-digit number)

35530406984431282737…81281733099617935361

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

7.106 × 10¹⁰¹(102-digit number)

71060813968862565475…62563466199235870719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.106 × 10¹⁰¹(102-digit number)

71060813968862565475…62563466199235870721

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

1.421 × 10¹⁰²(103-digit number)

14212162793772513095…25126932398471741439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.421 × 10¹⁰²(103-digit number)

14212162793772513095…25126932398471741441

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 345827

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 eba61eb82bce24aaa8c14e561dda5511a6ff365d8b16173cde252c2aba4ecb42

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 #345,827 on Chainz ↗