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Block #531,427

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2014, 12:09:33 PM Β· Difficulty 10.8941 Β· 6,264,919 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5168bd0c2236b8665f05a9eccdf5828ea518df26a81f5e9050ce3bb0bfc541f6
View on Chainz β†—

Height

#531,427

Difficulty

10.894093

Transactions

1

Size

209 B

Version

2

Bits

0ae4e346

Nonce

34,367,137

Timestamp

5/8/2014, 12:09:33 PM

Confirmations

6,264,919

Merkle Root

2bcc34dd1bc63c8ed4c6c6ffe8041fc8c002299365d35fe1b540b7bcf44fd7e3
Transactions (1)
Coinbase2bcc34dd1bc63c…40b7bcf44fd7e3
1 in β†’ 1 out8.4100 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.

1.058 Γ— 10¹⁰¹(102-digit number)
10589766683361388289…68625995318671042560
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
1.058 Γ— 10¹⁰¹(102-digit number)
10589766683361388289…68625995318671042561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.117 Γ— 10¹⁰¹(102-digit number)
21179533366722776579…37251990637342085121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.235 Γ— 10¹⁰¹(102-digit number)
42359066733445553159…74503981274684170241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.471 Γ— 10¹⁰¹(102-digit number)
84718133466891106319…49007962549368340481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.694 Γ— 10¹⁰²(103-digit number)
16943626693378221263…98015925098736680961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.388 Γ— 10¹⁰²(103-digit number)
33887253386756442527…96031850197473361921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.777 Γ— 10¹⁰²(103-digit number)
67774506773512885055…92063700394946723841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.355 Γ— 10¹⁰³(104-digit number)
13554901354702577011…84127400789893447681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.710 Γ— 10¹⁰³(104-digit number)
27109802709405154022…68254801579786895361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.421 Γ— 10¹⁰³(104-digit number)
54219605418810308044…36509603159573790721
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 531427

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 5168bd0c2236b8665f05a9eccdf5828ea518df26a81f5e9050ce3bb0bfc541f6

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 #531,427 on Chainz β†—
Circulating Supply:57,614,761 XPMΒ·at block #6,796,345 Β· updates every 60s
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