XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #50,963

Block #50,963

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 3:45:21 AM Β· Difficulty 8.8911 Β· 6,748,950 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09fdec5310865b406a74f68c82b1117fb4d7277dc013ccedd1d8545e1065e9f7
View on Chainz β†—

Height

#50,963

Difficulty

8.891055

Transactions

1

Size

199 B

Version

2

Bits

08e41c30

Nonce

2,140

Timestamp

7/16/2013, 3:45:21 AM

Confirmations

6,748,950

Merkle Root

39787531694216b71ad1b798370740e18d297b79a55980b71fc7e95f7f023c9d
Transactions (1)
Coinbase39787531694216…c7e95f7f023c9d
1 in β†’ 1 out12.6300 XPM110 B
AeTcmmqH…LrFchfe1
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.

2.222 Γ— 10⁹³(94-digit number)
22229401918934757279…94825621722737585040
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
2.222 Γ— 10⁹³(94-digit number)
22229401918934757279…94825621722737585041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.445 Γ— 10⁹³(94-digit number)
44458803837869514559…89651243445475170081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.891 Γ— 10⁹³(94-digit number)
88917607675739029118…79302486890950340161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.778 Γ— 10⁹⁴(95-digit number)
17783521535147805823…58604973781900680321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.556 Γ— 10⁹⁴(95-digit number)
35567043070295611647…17209947563801360641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.113 Γ— 10⁹⁴(95-digit number)
71134086140591223294…34419895127602721281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.422 Γ— 10⁹⁡(96-digit number)
14226817228118244658…68839790255205442561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.845 Γ— 10⁹⁡(96-digit number)
28453634456236489317…37679580510410885121
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 50963

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 09fdec5310865b406a74f68c82b1117fb4d7277dc013ccedd1d8545e1065e9f7

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 #50,963 on Chainz β†—
Circulating Supply:57,643,360 XPMΒ·at block #6,799,912 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