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Block #565,520

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/28/2014, 8:49:41 AM Β· Difficulty 10.9652 Β· 6,261,281 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d7128fff81d269d7bccb33ba4f93c0c3029b19812d05e01ac1afbf1573b6026c
View on Chainz β†—

Height

#565,520

Difficulty

10.965216

Transactions

1

Size

208 B

Version

2

Bits

0af71867

Nonce

472,453,767

Timestamp

5/28/2014, 8:49:41 AM

Confirmations

6,261,281

Merkle Root

c2ab7d7374bc28d20ef206f7decc21c82a3ab68bfd2301f3ed5a4a2bbc8f0b8d
Transactions (1)
Coinbasec2ab7d7374bc28…5a4a2bbc8f0b8d
1 in β†’ 1 out8.3000 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.

1.359 Γ— 10¹⁰⁰(101-digit number)
13598503808711920117…47309460616767897600
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.359 Γ— 10¹⁰⁰(101-digit number)
13598503808711920117…47309460616767897599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.719 Γ— 10¹⁰⁰(101-digit number)
27197007617423840234…94618921233535795199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.439 Γ— 10¹⁰⁰(101-digit number)
54394015234847680468…89237842467071590399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.087 Γ— 10¹⁰¹(102-digit number)
10878803046969536093…78475684934143180799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.175 Γ— 10¹⁰¹(102-digit number)
21757606093939072187…56951369868286361599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.351 Γ— 10¹⁰¹(102-digit number)
43515212187878144375…13902739736572723199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.703 Γ— 10¹⁰¹(102-digit number)
87030424375756288750…27805479473145446399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.740 Γ— 10¹⁰²(103-digit number)
17406084875151257750…55610958946290892799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.481 Γ— 10¹⁰²(103-digit number)
34812169750302515500…11221917892581785599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.962 Γ— 10¹⁰²(103-digit number)
69624339500605031000…22443835785163571199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 565520

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 d7128fff81d269d7bccb33ba4f93c0c3029b19812d05e01ac1afbf1573b6026c

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 #565,520 on Chainz β†—
Circulating Supply:57,858,571 XPMΒ·at block #6,826,800 Β· updates every 60s
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