XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #51,529

Block #51,529

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 6:13:42 AM Β· Difficulty 8.8997 Β· 6,760,735 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8cb434d3b881210fb4f3cf50cc7c1b4ba882ad3f00e4a462499ce52fd032626e
View on Chainz β†—

Height

#51,529

Difficulty

8.899730

Transactions

1

Size

198 B

Version

2

Bits

08e654b0

Nonce

186

Timestamp

7/16/2013, 6:13:42 AM

Confirmations

6,760,735

Merkle Root

539e6e5ab3dbe65c97598274b15c304df2b0fbf3e4f21b31b446c820a968abc7
Transactions (1)
Coinbase539e6e5ab3dbe6…46c820a968abc7
1 in β†’ 1 out12.6100 XPM110 B
Aad6Dfti…3wP7iQmg
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.

1.223 Γ— 10⁹⁰(91-digit number)
12233103221671350784…44473432572512542000
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
1.223 Γ— 10⁹⁰(91-digit number)
12233103221671350784…44473432572512542001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.446 Γ— 10⁹⁰(91-digit number)
24466206443342701569…88946865145025084001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.893 Γ— 10⁹⁰(91-digit number)
48932412886685403138…77893730290050168001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.786 Γ— 10⁹⁰(91-digit number)
97864825773370806277…55787460580100336001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.957 Γ— 10⁹¹(92-digit number)
19572965154674161255…11574921160200672001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.914 Γ— 10⁹¹(92-digit number)
39145930309348322510…23149842320401344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.829 Γ— 10⁹¹(92-digit number)
78291860618696645021…46299684640802688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.565 Γ— 10⁹²(93-digit number)
15658372123739329004…92599369281605376001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 51529

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 8cb434d3b881210fb4f3cf50cc7c1b4ba882ad3f00e4a462499ce52fd032626e

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 #51,529 on Chainz β†—
Circulating Supply:57,742,129 XPMΒ·at block #6,812,263 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy