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Block #362,599

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/16/2014, 7:57:39 PM Β· Difficulty 10.4152 Β· 6,431,969 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a737ea5f80ccaaa33f5381d5f87808ac99ddb7d45cc9bd9059a05d2809aa79d5
View on Chainz β†—

Height

#362,599

Difficulty

10.415245

Transactions

1

Size

202 B

Version

2

Bits

0a6a4d85

Nonce

62,521

Timestamp

1/16/2014, 7:57:39 PM

Confirmations

6,431,969

Merkle Root

65ed5fc36b5f2ad1ab57018a004c7fad892d25302e2cdca116be0e381c92cfc7
Transactions (1)
Coinbase65ed5fc36b5f2a…be0e381c92cfc7
1 in β†’ 1 out9.2000 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.

1.982 Γ— 10⁹⁹(100-digit number)
19823248334091830412…59446292154808898720
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
1.982 Γ— 10⁹⁹(100-digit number)
19823248334091830412…59446292154808898721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.964 Γ— 10⁹⁹(100-digit number)
39646496668183660824…18892584309617797441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.929 Γ— 10⁹⁹(100-digit number)
79292993336367321648…37785168619235594881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.585 Γ— 10¹⁰⁰(101-digit number)
15858598667273464329…75570337238471189761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.171 Γ— 10¹⁰⁰(101-digit number)
31717197334546928659…51140674476942379521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.343 Γ— 10¹⁰⁰(101-digit number)
63434394669093857318…02281348953884759041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.268 Γ— 10¹⁰¹(102-digit number)
12686878933818771463…04562697907769518081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.537 Γ— 10¹⁰¹(102-digit number)
25373757867637542927…09125395815539036161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.074 Γ— 10¹⁰¹(102-digit number)
50747515735275085855…18250791631078072321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.014 Γ— 10¹⁰²(103-digit number)
10149503147055017171…36501583262156144641
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 362599

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 a737ea5f80ccaaa33f5381d5f87808ac99ddb7d45cc9bd9059a05d2809aa79d5

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 #362,599 on Chainz β†—
Circulating Supply:57,600,588 XPMΒ·at block #6,794,567 Β· updates every 60s
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