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Block #83,405

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 3:24:15 AM · Difficulty 9.2674 · 6,716,979 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

159f64bad5044ba035e14546ec301ae43dbd3f57487ee4df479b9ac83b38f55f

View on Chainz ↗

Height

#83,405

Difficulty

9.267396

Transactions

Size

207 B

Version

Bits

09447416

Nonce

730

Timestamp

7/26/2013, 3:24:15 AM

Confirmations

6,716,979

Merkle Root

fcdc6f365682a555b9c303df2d816aba7a82c0b05f3da0c3ee039a9587c727f3

Transactions (1)

Coinbasefcdc6f365682a5…039a9587c727f3

1 in → 1 out11.6300 XPM110 B

AZiGXLkm…3uFqRmWV

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.

1.770 × 10¹¹¹(112-digit number)

17706485525425271122…22733713531443917840

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

1.770 × 10¹¹¹(112-digit number)

17706485525425271122…22733713531443917839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.770 × 10¹¹¹(112-digit number)

17706485525425271122…22733713531443917841

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

3.541 × 10¹¹¹(112-digit number)

35412971050850542244…45467427062887835679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.541 × 10¹¹¹(112-digit number)

35412971050850542244…45467427062887835681

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

7.082 × 10¹¹¹(112-digit number)

70825942101701084488…90934854125775671359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.082 × 10¹¹¹(112-digit number)

70825942101701084488…90934854125775671361

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

1.416 × 10¹¹²(113-digit number)

14165188420340216897…81869708251551342719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.416 × 10¹¹²(113-digit number)

14165188420340216897…81869708251551342721

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

2.833 × 10¹¹²(113-digit number)

28330376840680433795…63739416503102685439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 83405

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 159f64bad5044ba035e14546ec301ae43dbd3f57487ee4df479b9ac83b38f55f

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 #83,405 on Chainz ↗