Home/Chain Registry/Block #269,752

Block #269,752

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 10:28:11 AM · Difficulty 9.9523 · 6,557,461 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41c43fca2c7967192d3b4eeee8c4a4ffca07404414c71077d3ee26e05da39670

View on Chainz ↗

Height

#269,752

Difficulty

9.952299

Transactions

Size

1.35 KB

Version

Bits

09f3c9e1

Nonce

335,497

Timestamp

11/23/2013, 10:28:11 AM

Confirmations

6,557,461

Merkle Root

2776ef5dbc435f22d8888d560f4c41ff131e66549d90af030702a9d68f75206c

Transactions (1)

Coinbase2776ef5dbc435f…02a9d68f75206c

1 in → 36 out10.0600 XPM1.26 KB

AFqKfjez…qX9Ace3g APVGazMT…cDCk2nwA AMbCuLHZ…WSoStwkc ANmkKL2U…jPxj1Qs3 APeshfYV…3PKcKMKH

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.

5.121 × 10⁹⁶(97-digit number)

51216143694169723154…53986855757776605440

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

5.121 × 10⁹⁶(97-digit number)

51216143694169723154…53986855757776605439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.121 × 10⁹⁶(97-digit number)

51216143694169723154…53986855757776605441

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 × 10⁹⁷(98-digit number)

10243228738833944630…07973711515553210879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.024 × 10⁹⁷(98-digit number)

10243228738833944630…07973711515553210881

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

2.048 × 10⁹⁷(98-digit number)

20486457477667889261…15947423031106421759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.048 × 10⁹⁷(98-digit number)

20486457477667889261…15947423031106421761

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

4.097 × 10⁹⁷(98-digit number)

40972914955335778523…31894846062212843519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.097 × 10⁹⁷(98-digit number)

40972914955335778523…31894846062212843521

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

8.194 × 10⁹⁷(98-digit number)

81945829910671557047…63789692124425687039

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 269752

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 41c43fca2c7967192d3b4eeee8c4a4ffca07404414c71077d3ee26e05da39670

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 #269,752 on Chainz ↗

Block #269,752

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