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Block #521,768

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2014, 4:07:10 PM Β· Difficulty 10.8636 Β· 6,303,801 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
464deea79fe57a740563bfd605c08f5bfe01bcec724659c95131ed3b27c2f35b
View on Chainz β†—

Height

#521,768

Difficulty

10.863619

Transactions

1

Size

199 B

Version

2

Bits

0add1628

Nonce

65,666

Timestamp

5/2/2014, 4:07:10 PM

Confirmations

6,303,801

Merkle Root

b4b4fe8c12e0b1e4fca625d6c2eebd577e5f0d23c213cc5d2cc5fe53eaabbf38
Transactions (1)
Coinbaseb4b4fe8c12e0b1…c5fe53eaabbf38
1 in β†’ 1 out8.4600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

9.418 Γ— 10⁹²(93-digit number)
94188125404453297992…84617260434785988580
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
9.418 Γ— 10⁹²(93-digit number)
94188125404453297992…84617260434785988581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.883 Γ— 10⁹³(94-digit number)
18837625080890659598…69234520869571977161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.767 Γ— 10⁹³(94-digit number)
37675250161781319197…38469041739143954321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.535 Γ— 10⁹³(94-digit number)
75350500323562638394…76938083478287908641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.507 Γ— 10⁹⁴(95-digit number)
15070100064712527678…53876166956575817281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.014 Γ— 10⁹⁴(95-digit number)
30140200129425055357…07752333913151634561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.028 Γ— 10⁹⁴(95-digit number)
60280400258850110715…15504667826303269121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.205 Γ— 10⁹⁡(96-digit number)
12056080051770022143…31009335652606538241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.411 Γ— 10⁹⁡(96-digit number)
24112160103540044286…62018671305213076481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.822 Γ— 10⁹⁡(96-digit number)
48224320207080088572…24037342610426152961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.644 Γ— 10⁹⁡(96-digit number)
96448640414160177144…48074685220852305921
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 521768

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 464deea79fe57a740563bfd605c08f5bfe01bcec724659c95131ed3b27c2f35b

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 #521,768 on Chainz β†—
Circulating Supply:57,848,654 XPMΒ·at block #6,825,568 Β· updates every 60s
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