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Block #605,188

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/28/2014, 8:28:54 AM Β· Difficulty 10.9098 Β· 6,221,990 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5b026c8177c3ec62663e00d18eaa07e3665a701e03fc0cc1fb433c64f799a042
View on Chainz β†—

Height

#605,188

Difficulty

10.909798

Transactions

1

Size

208 B

Version

2

Bits

0ae8e88c

Nonce

96,410,145

Timestamp

6/28/2014, 8:28:54 AM

Confirmations

6,221,990

Merkle Root

b00bf4daaa8c3232b5ea72935476ea7e05a3b1492ca39481918f4d82589e4438
Transactions (1)
Coinbaseb00bf4daaa8c32…8f4d82589e4438
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.

3.394 Γ— 10⁹⁹(100-digit number)
33944615822733455153…11409799561263034880
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
3.394 Γ— 10⁹⁹(100-digit number)
33944615822733455153…11409799561263034881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.788 Γ— 10⁹⁹(100-digit number)
67889231645466910306…22819599122526069761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.357 Γ— 10¹⁰⁰(101-digit number)
13577846329093382061…45639198245052139521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.715 Γ— 10¹⁰⁰(101-digit number)
27155692658186764122…91278396490104279041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.431 Γ— 10¹⁰⁰(101-digit number)
54311385316373528244…82556792980208558081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.086 Γ— 10¹⁰¹(102-digit number)
10862277063274705648…65113585960417116161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.172 Γ— 10¹⁰¹(102-digit number)
21724554126549411297…30227171920834232321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.344 Γ— 10¹⁰¹(102-digit number)
43449108253098822595…60454343841668464641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.689 Γ— 10¹⁰¹(102-digit number)
86898216506197645191…20908687683336929281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.737 Γ— 10¹⁰²(103-digit number)
17379643301239529038…41817375366673858561
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 605188

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 5b026c8177c3ec62663e00d18eaa07e3665a701e03fc0cc1fb433c64f799a042

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 #605,188 on Chainz β†—
Circulating Supply:57,861,519 XPMΒ·at block #6,827,177 Β· updates every 60s
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