Home/Chain Registry/Block #164,059

Block #164,059

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/14/2013, 10:35:15 AM · Difficulty 9.8616 · 6,662,924 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9a7d438aecf0f090113bb9e4ee2f9e873d557cf1ec17a2d996ed3409a2c6283

View on Chainz ↗

Height

#164,059

Difficulty

9.861572

Transactions

Size

425 B

Version

Bits

09dc9001

Nonce

176,209

Timestamp

9/14/2013, 10:35:15 AM

Confirmations

6,662,924

Merkle Root

fd2e223014180e66043b54b7507966a0593c15c8961b1e18ca4f298d2d7e24d5

Transactions (2)

Coinbase366389a5bdd68e…e41d7e6f55fcbc

1 in → 1 out10.2800 XPM109 B

AcQ2wdJd…jqwoAdmB

c106cc5d0fa514…203e73924ec3d6

1 in → 2 out10.0150 XPM227 B

AFrfL9P3…xWP9CZ7C AdbJFypX…APWBtUDC

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.

1.134 × 10⁹²(93-digit number)

11345880144865317454…47128596200010734560

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

1.134 × 10⁹²(93-digit number)

11345880144865317454…47128596200010734559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.134 × 10⁹²(93-digit number)

11345880144865317454…47128596200010734561

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

2.269 × 10⁹²(93-digit number)

22691760289730634908…94257192400021469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.269 × 10⁹²(93-digit number)

22691760289730634908…94257192400021469121

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

4.538 × 10⁹²(93-digit number)

45383520579461269816…88514384800042938239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.538 × 10⁹²(93-digit number)

45383520579461269816…88514384800042938241

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

9.076 × 10⁹²(93-digit number)

90767041158922539632…77028769600085876479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.076 × 10⁹²(93-digit number)

90767041158922539632…77028769600085876481

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

1.815 × 10⁹³(94-digit number)

18153408231784507926…54057539200171752959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.815 × 10⁹³(94-digit number)

18153408231784507926…54057539200171752961

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 164059

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 c9a7d438aecf0f090113bb9e4ee2f9e873d557cf1ec17a2d996ed3409a2c6283

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 #164,059 on Chainz ↗

Block #164,059

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