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Block #604,212

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/27/2014, 3:11:18 PM Β· Difficulty 10.9108 Β· 6,221,494 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b79ce5fd8443e4c04cd2197a2f72ad4e9c15205e9a7163abd5c0295ac86dd4e4
View on Chainz β†—

Height

#604,212

Difficulty

10.910848

Transactions

1

Size

207 B

Version

2

Bits

0ae92d50

Nonce

183,073,451

Timestamp

6/27/2014, 3:11:18 PM

Confirmations

6,221,494

Merkle Root

bdc8ae42767cb88c00150d476646ca860eee2b22b57d59150e2b7746842ef4dd
Transactions (1)
Coinbasebdc8ae42767cb8…2b7746842ef4dd
1 in β†’ 1 out8.3900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

6.476 Γ— 10⁹⁷(98-digit number)
64760414012590438707…24890566991964178120
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
6.476 Γ— 10⁹⁷(98-digit number)
64760414012590438707…24890566991964178121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.295 Γ— 10⁹⁸(99-digit number)
12952082802518087741…49781133983928356241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.590 Γ— 10⁹⁸(99-digit number)
25904165605036175483…99562267967856712481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.180 Γ— 10⁹⁸(99-digit number)
51808331210072350966…99124535935713424961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.036 Γ— 10⁹⁹(100-digit number)
10361666242014470193…98249071871426849921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.072 Γ— 10⁹⁹(100-digit number)
20723332484028940386…96498143742853699841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.144 Γ— 10⁹⁹(100-digit number)
41446664968057880772…92996287485707399681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.289 Γ— 10⁹⁹(100-digit number)
82893329936115761545…85992574971414799361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.657 Γ— 10¹⁰⁰(101-digit number)
16578665987223152309…71985149942829598721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.315 Γ— 10¹⁰⁰(101-digit number)
33157331974446304618…43970299885659197441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.631 Γ— 10¹⁰⁰(101-digit number)
66314663948892609236…87940599771318394881
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 604212

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 b79ce5fd8443e4c04cd2197a2f72ad4e9c15205e9a7163abd5c0295ac86dd4e4

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 #604,212 on Chainz β†—
Circulating Supply:57,849,751 XPMΒ·at block #6,825,705 Β· updates every 60s
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