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Block #42,904

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 7:42:08 PM · Difficulty 8.6315 · 6,771,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

777d3e51e86c80ed06b3f95fbdb2a449f417fdb746bd010f8adb5e16b31ff9d7

View on Chainz ↗

Height

#42,904

Difficulty

8.631464

Transactions

Size

358 B

Version

Bits

08a1a7a8

Nonce

136

Timestamp

7/14/2013, 7:42:08 PM

Confirmations

6,771,128

Merkle Root

d2af566f5fa3a29106fc594e5df43e8a5a0468210677bfeb29004b27993e83da

Transactions (2)

Coinbasee7f2240778cb59…7ace7cf794cd8e

1 in → 1 out13.4100 XPM110 B

ALBHaoyu…dkaDEyRu

2f1638d85ea31c…53d037feae779a

1 in → 1 out14.3200 XPM157 B

AHkEa2Pq…tUzrKxgF

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.

5.124 × 10⁹⁷(98-digit number)

51242508934299546001…06089056176157476720

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

5.124 × 10⁹⁷(98-digit number)

51242508934299546001…06089056176157476719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.124 × 10⁹⁷(98-digit number)

51242508934299546001…06089056176157476721

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

1.024 × 10⁹⁸(99-digit number)

10248501786859909200…12178112352314953439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.024 × 10⁹⁸(99-digit number)

10248501786859909200…12178112352314953441

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

2.049 × 10⁹⁸(99-digit number)

20497003573719818400…24356224704629906879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.049 × 10⁹⁸(99-digit number)

20497003573719818400…24356224704629906881

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

4.099 × 10⁹⁸(99-digit number)

40994007147439636800…48712449409259813759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.099 × 10⁹⁸(99-digit number)

40994007147439636800…48712449409259813761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 42904

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 777d3e51e86c80ed06b3f95fbdb2a449f417fdb746bd010f8adb5e16b31ff9d7

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 #42,904 on Chainz ↗

Block #42,904

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