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Home/Chain Registry/Block #2,862,481

Block #2,862,481

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/1/2018, 9:38:09 AM Β· Difficulty 11.6749 Β· 3,982,205 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0e52fa3ddb4324513f50b89532feb61b7f73af6635bb20366eb1453b2e31c7e3
View on Chainz β†—

Difficulty

11.674924

Transactions

1

Size

200 B

Version

2

Bits

0bacc7cf

Nonce

1,970,781,596

Timestamp

10/1/2018, 9:38:09 AM

Confirmations

3,982,205

Merkle Root

337aba23aa689207d60fa0b7dd3a37994aa4b4a179be380409cfcb439a539d79
Transactions (1)
Coinbase337aba23aa6892…cfcb439a539d79
1 in β†’ 1 out7.3200 XPM110 B
AcuJxaWc…6vbt3urU
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.518 Γ— 10⁹⁴(95-digit number)
15181600584779344776…67796354553223104000
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
1.518 Γ— 10⁹⁴(95-digit number)
15181600584779344776…67796354553223104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.036 Γ— 10⁹⁴(95-digit number)
30363201169558689552…35592709106446208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.072 Γ— 10⁹⁴(95-digit number)
60726402339117379105…71185418212892416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.214 Γ— 10⁹⁡(96-digit number)
12145280467823475821…42370836425784832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.429 Γ— 10⁹⁡(96-digit number)
24290560935646951642…84741672851569664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.858 Γ— 10⁹⁡(96-digit number)
48581121871293903284…69483345703139328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.716 Γ— 10⁹⁡(96-digit number)
97162243742587806568…38966691406278656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.943 Γ— 10⁹⁢(97-digit number)
19432448748517561313…77933382812557312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.886 Γ— 10⁹⁢(97-digit number)
38864897497035122627…55866765625114624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.772 Γ— 10⁹⁢(97-digit number)
77729794994070245254…11733531250229248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.554 Γ— 10⁹⁷(98-digit number)
15545958998814049050…23467062500458496001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2862481

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 0e52fa3ddb4324513f50b89532feb61b7f73af6635bb20366eb1453b2e31c7e3

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 β†’ Debug Window β†’ 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 #2,862,481 on Chainz β†—
Circulating Supply:58,001,896 XPMΒ·at block #6,844,685 Β· updates every 60s
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