Home/Chain Registry/Block #848,824

Block #848,824

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2014, 9:02:43 AM · Difficulty 10.9715 · 5,995,673 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

89ebbdded11c4863a3928adf8923d9eae06953170cc2ecea968bca05211df694

View on Chainz ↗

Height

#848,824

Difficulty

10.971497

Transactions

Size

879 B

Version

Bits

0af8b400

Nonce

310,380,357

Timestamp

12/11/2014, 9:02:43 AM

Confirmations

5,995,673

Merkle Root

2616538067d86ab1e03837d63fabac5b1b61a119203ee9b490c869ca4b6a6487

Transactions (4)

Coinbase799f954f5ab3df…49a865dd6904a2

1 in → 1 out8.3300 XPM110 B

AU9TFoPV…PzWcCbWH

19d326e061a481…baa9d00c0055df

1 in → 2 out631.3800 XPM227 B

AMN6qDkt…VuvvTq6f AGCfDPXx…krjoRcnU

1e876321ef7be5…e79c74c17d0262

1 in → 2 out0.0914 XPM225 B

AZpg5HNM…XwHhvkvQ ALKpzCtY…LgPmeRi3

0d367ceb01cf48…cda55706ca954c

1 in → 2 out0.0903 XPM227 B

AS9vQJqj…SEWjREvr ASsenvcS…CLb6ALYM

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.

1.661 × 10⁹⁵(96-digit number)

16614563226635572404…03404392704708280320

Discovered Prime Numbers

p_k = 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.

origin + 1

1.661 × 10⁹⁵(96-digit number)

16614563226635572404…03404392704708280321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.322 × 10⁹⁵(96-digit number)

33229126453271144808…06808785409416560641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.645 × 10⁹⁵(96-digit number)

66458252906542289616…13617570818833121281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.329 × 10⁹⁶(97-digit number)

13291650581308457923…27235141637666242561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.658 × 10⁹⁶(97-digit number)

26583301162616915846…54470283275332485121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.316 × 10⁹⁶(97-digit number)

53166602325233831693…08940566550664970241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.063 × 10⁹⁷(98-digit number)

10633320465046766338…17881133101329940481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.126 × 10⁹⁷(98-digit number)

21266640930093532677…35762266202659880961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.253 × 10⁹⁷(98-digit number)

42533281860187065354…71524532405319761921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.506 × 10⁹⁷(98-digit number)

85066563720374130709…43049064810639523841

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 848824

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 89ebbdded11c4863a3928adf8923d9eae06953170cc2ecea968bca05211df694

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 #848,824 on Chainz ↗

Block #848,824

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