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Block #526,533

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2014, 11:00:58 AM Β· Difficulty 10.8827 Β· 6,275,063 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8c415d8eb9f8267cb5d2cb53d84b48705a8e22fc31120e0bdad0f09893cd23bc
View on Chainz β†—

Height

#526,533

Difficulty

10.882697

Transactions

1

Size

208 B

Version

2

Bits

0ae1f870

Nonce

10,502,657

Timestamp

5/5/2014, 11:00:58 AM

Confirmations

6,275,063

Merkle Root

99c3946e69ba4852da8943b3add9f574baa64ea5bbf9cfa911d788fdac1c23ad
Transactions (1)
Coinbase99c3946e69ba48…d788fdac1c23ad
1 in β†’ 1 out8.4300 XPM116 B
AbwWkWZt…kawDhufa
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.

2.447 Γ— 10⁹⁸(99-digit number)
24470930377819560503…36658428830306902420
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
2.447 Γ— 10⁹⁸(99-digit number)
24470930377819560503…36658428830306902421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.894 Γ— 10⁹⁸(99-digit number)
48941860755639121007…73316857660613804841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.788 Γ— 10⁹⁸(99-digit number)
97883721511278242015…46633715321227609681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.957 Γ— 10⁹⁹(100-digit number)
19576744302255648403…93267430642455219361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.915 Γ— 10⁹⁹(100-digit number)
39153488604511296806…86534861284910438721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.830 Γ— 10⁹⁹(100-digit number)
78306977209022593612…73069722569820877441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.566 Γ— 10¹⁰⁰(101-digit number)
15661395441804518722…46139445139641754881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.132 Γ— 10¹⁰⁰(101-digit number)
31322790883609037444…92278890279283509761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.264 Γ— 10¹⁰⁰(101-digit number)
62645581767218074889…84557780558567019521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.252 Γ— 10¹⁰¹(102-digit number)
12529116353443614977…69115561117134039041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.505 Γ— 10¹⁰¹(102-digit number)
25058232706887229955…38231122234268078081
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 526533

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 8c415d8eb9f8267cb5d2cb53d84b48705a8e22fc31120e0bdad0f09893cd23bc

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 #526,533 on Chainz β†—
Circulating Supply:57,656,847 XPMΒ·at block #6,801,595 Β· updates every 60s
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