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Home/Chain Registry/Block #534,819

Block #534,819

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/10/2014, 1:24:08 PM Β· Difficulty 10.9030 Β· 6,270,402 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ca6148217d364ea4bda9da86d376a7d6b7b69db4abe8c7da3aee5f958c0ed65a
View on Chainz β†—

Height

#534,819

Difficulty

10.903017

Transactions

1

Size

209 B

Version

2

Bits

0ae72c1f

Nonce

94,001,916

Timestamp

5/10/2014, 1:24:08 PM

Confirmations

6,270,402

Merkle Root

4df599376dbfaf44f03ae1aa9c23a9045b077e1d0f5738f2772027ffd7d3a6c4
Transactions (1)
Coinbase4df599376dbfaf…2027ffd7d3a6c4
1 in β†’ 1 out8.4000 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.

1.766 Γ— 10¹⁰¹(102-digit number)
17660097106026064592…45452957481749391360
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
1.766 Γ— 10¹⁰¹(102-digit number)
17660097106026064592…45452957481749391361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.532 Γ— 10¹⁰¹(102-digit number)
35320194212052129185…90905914963498782721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.064 Γ— 10¹⁰¹(102-digit number)
70640388424104258371…81811829926997565441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.412 Γ— 10¹⁰²(103-digit number)
14128077684820851674…63623659853995130881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.825 Γ— 10¹⁰²(103-digit number)
28256155369641703348…27247319707990261761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.651 Γ— 10¹⁰²(103-digit number)
56512310739283406697…54494639415980523521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.130 Γ— 10¹⁰³(104-digit number)
11302462147856681339…08989278831961047041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.260 Γ— 10¹⁰³(104-digit number)
22604924295713362678…17978557663922094081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.520 Γ— 10¹⁰³(104-digit number)
45209848591426725357…35957115327844188161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.041 Γ— 10¹⁰³(104-digit number)
90419697182853450715…71914230655688376321
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 534819

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 ca6148217d364ea4bda9da86d376a7d6b7b69db4abe8c7da3aee5f958c0ed65a

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 #534,819 on Chainz β†—
Circulating Supply:57,685,842 XPMΒ·at block #6,805,220 Β· updates every 60s
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