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Block #605,472

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/28/2014, 1:08:50 PM Β· Difficulty 10.9099 Β· 6,220,843 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ee02d3d7c3411e350aae7c08807517f723fea32717ff9c928ea0fd0238c9fb4d
View on Chainz β†—

Height

#605,472

Difficulty

10.909910

Transactions

1

Size

244 B

Version

2

Bits

0ae8efde

Nonce

272,945,366

Timestamp

6/28/2014, 1:08:50 PM

Confirmations

6,220,843

Merkle Root

dbaf668415d78020a216b51ec92c585e5aeb903f61ef6ce33da3a3dc88f86ab8
Transactions (1)
Coinbasedbaf668415d780…a3a3dc88f86ab8
1 in β†’ 2 out8.3900 XPM152 B
AHtZq5bT…9EBTtkMYALPu3s2c…EJXLjVFh
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.

2.837 Γ— 10⁹⁹(100-digit number)
28372358623374079926…77996392614739845120
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
2.837 Γ— 10⁹⁹(100-digit number)
28372358623374079926…77996392614739845121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.674 Γ— 10⁹⁹(100-digit number)
56744717246748159853…55992785229479690241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.134 Γ— 10¹⁰⁰(101-digit number)
11348943449349631970…11985570458959380481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.269 Γ— 10¹⁰⁰(101-digit number)
22697886898699263941…23971140917918760961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.539 Γ— 10¹⁰⁰(101-digit number)
45395773797398527883…47942281835837521921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.079 Γ— 10¹⁰⁰(101-digit number)
90791547594797055766…95884563671675043841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.815 Γ— 10¹⁰¹(102-digit number)
18158309518959411153…91769127343350087681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.631 Γ— 10¹⁰¹(102-digit number)
36316619037918822306…83538254686700175361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.263 Γ— 10¹⁰¹(102-digit number)
72633238075837644612…67076509373400350721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.452 Γ— 10¹⁰²(103-digit number)
14526647615167528922…34153018746800701441
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 605472

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 ee02d3d7c3411e350aae7c08807517f723fea32717ff9c928ea0fd0238c9fb4d

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 #605,472 on Chainz β†—
Circulating Supply:57,854,658 XPMΒ·at block #6,826,314 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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