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Home/Chain Registry/Block #2,644,535

Block #2,644,535

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 1:12:17 PM Β· Difficulty 11.7115 Β· 4,189,423 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1ac61745d1a18d55e2c8f6cf8b3446c706c5be8de09c1e129100c228ba42ca2c
View on Chainz β†—

Difficulty

11.711508

Transactions

1

Size

200 B

Version

2

Bits

0bb6255d

Nonce

46,405,386

Timestamp

5/2/2018, 1:12:17 PM

Confirmations

4,189,423

Merkle Root

48f499104e5cbbd3015db9ffdb460303a068f0dcffcf945a0edca1d4f28771cc
Transactions (1)
Coinbase48f499104e5cbb…dca1d4f28771cc
1 in β†’ 1 out7.2800 XPM110 B
AenPRtKa…uKAhUh34
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.

2.106 Γ— 10⁹⁴(95-digit number)
21062952510910244090…61258810247484199980
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
2.106 Γ— 10⁹⁴(95-digit number)
21062952510910244090…61258810247484199981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.212 Γ— 10⁹⁴(95-digit number)
42125905021820488180…22517620494968399961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.425 Γ— 10⁹⁴(95-digit number)
84251810043640976361…45035240989936799921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.685 Γ— 10⁹⁡(96-digit number)
16850362008728195272…90070481979873599841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.370 Γ— 10⁹⁡(96-digit number)
33700724017456390544…80140963959747199681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.740 Γ— 10⁹⁡(96-digit number)
67401448034912781089…60281927919494399361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.348 Γ— 10⁹⁢(97-digit number)
13480289606982556217…20563855838988798721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.696 Γ— 10⁹⁢(97-digit number)
26960579213965112435…41127711677977597441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.392 Γ— 10⁹⁢(97-digit number)
53921158427930224871…82255423355955194881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.078 Γ— 10⁹⁷(98-digit number)
10784231685586044974…64510846711910389761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.156 Γ— 10⁹⁷(98-digit number)
21568463371172089948…29021693423820779521
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 2644535

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 1ac61745d1a18d55e2c8f6cf8b3446c706c5be8de09c1e129100c228ba42ca2c

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 #2,644,535 on Chainz β†—
Circulating Supply:57,915,892 XPMΒ·at block #6,833,957 Β· updates every 60s
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