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Block #449,028

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/18/2014, 9:31:21 AM Β· Difficulty 10.3666 Β· 6,351,221 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8fc60635c8eb6d2e9e7d22a75e01347ed6cbb9d2727497070ed78d3778490e22
View on Chainz β†—

Height

#449,028

Difficulty

10.366564

Transactions

1

Size

199 B

Version

2

Bits

0a5dd720

Nonce

553,689

Timestamp

3/18/2014, 9:31:21 AM

Confirmations

6,351,221

Merkle Root

0544c92c472ab908bbb60276aba92787c50a51cb32bbcc7d02b24535d8f44f2d
Transactions (1)
Coinbase0544c92c472ab9…b24535d8f44f2d
1 in β†’ 1 out9.2900 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.238 Γ— 10⁹³(94-digit number)
22383630207127842363…12528093564929034250
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
2.238 Γ— 10⁹³(94-digit number)
22383630207127842363…12528093564929034251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.476 Γ— 10⁹³(94-digit number)
44767260414255684726…25056187129858068501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.953 Γ— 10⁹³(94-digit number)
89534520828511369452…50112374259716137001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.790 Γ— 10⁹⁴(95-digit number)
17906904165702273890…00224748519432274001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.581 Γ— 10⁹⁴(95-digit number)
35813808331404547780…00449497038864548001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.162 Γ— 10⁹⁴(95-digit number)
71627616662809095561…00898994077729096001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.432 Γ— 10⁹⁡(96-digit number)
14325523332561819112…01797988155458192001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.865 Γ— 10⁹⁡(96-digit number)
28651046665123638224…03595976310916384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.730 Γ— 10⁹⁡(96-digit number)
57302093330247276449…07191952621832768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.146 Γ— 10⁹⁢(97-digit number)
11460418666049455289…14383905243665536001
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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 449028

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 8fc60635c8eb6d2e9e7d22a75e01347ed6cbb9d2727497070ed78d3778490e22

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 #449,028 on Chainz β†—
Circulating Supply:57,646,046 XPMΒ·at block #6,800,248 Β· updates every 60s
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