Home/Chain Registry/Block #269,849

Block #269,849

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 12:32:27 PM · Difficulty 9.9521 · 6,545,055 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a92ccb45ee615ffe3ae8ee0cfbab445adfbe0f425787b35cdcd5a6d4fafdf2cc

View on Chainz ↗

Height

#269,849

Difficulty

9.952051

Transactions

Size

213 B

Version

Bits

09f3b9a4

Nonce

987

Timestamp

11/23/2013, 12:32:27 PM

Confirmations

6,545,055

Merkle Root

da2d4b1cc56067f1a069f0ed82d2dda56d1ac98cb85d8d6c51c841dff6ed9197

Transactions (1)

Coinbaseda2d4b1cc56067…c841dff6ed9197

1 in → 1 out10.0800 XPM116 B

AcLBm5Z9…S683d7c3

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.

7.367 × 10¹¹⁰(111-digit number)

73676268926425179033…21900977234892554240

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

7.367 × 10¹¹⁰(111-digit number)

73676268926425179033…21900977234892554239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.367 × 10¹¹⁰(111-digit number)

73676268926425179033…21900977234892554241

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

1.473 × 10¹¹¹(112-digit number)

14735253785285035806…43801954469785108479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.473 × 10¹¹¹(112-digit number)

14735253785285035806…43801954469785108481

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

2.947 × 10¹¹¹(112-digit number)

29470507570570071613…87603908939570216959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.947 × 10¹¹¹(112-digit number)

29470507570570071613…87603908939570216961

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

5.894 × 10¹¹¹(112-digit number)

58941015141140143227…75207817879140433919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.894 × 10¹¹¹(112-digit number)

58941015141140143227…75207817879140433921

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

1.178 × 10¹¹²(113-digit number)

11788203028228028645…50415635758280867839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.178 × 10¹¹²(113-digit number)

11788203028228028645…50415635758280867841

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 269849

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 a92ccb45ee615ffe3ae8ee0cfbab445adfbe0f425787b35cdcd5a6d4fafdf2cc

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 #269,849 on Chainz ↗

Block #269,849

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