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Block #79,141

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/23/2013, 7:29:54 AM Β· Difficulty 9.2391 Β· 6,716,749 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e2f83cf660fc25f2dc3ef19110ef7e8d1687fece4c3774c306fcace711eba30
View on Chainz β†—

Height

#79,141

Difficulty

9.239133

Transactions

2

Size

574 B

Version

2

Bits

093d37da

Nonce

550

Timestamp

7/23/2013, 7:29:54 AM

Confirmations

6,716,749

Merkle Root

228423feaf56e090fac7d3ffdcdde116e7ca50368258b70e36b23f5bf1961a61
Transactions (2)
Coinbase38d02e5c80b505…82dc89ed949902
1 in β†’ 1 out11.7100 XPM110 B
AQAnpJv4…JCMqS3zE
c51ee8e14931c5…dae7ff075fc6a5
2 in β†’ 2 out500.0400 XPM373 B
AXxNdKL3…Z3TUkCMLAcydZnwj…WuXWc3wi
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.

7.701 Γ— 10⁹⁢(97-digit number)
77012542151343399194…97724653989298835960
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
7.701 Γ— 10⁹⁢(97-digit number)
77012542151343399194…97724653989298835961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.540 Γ— 10⁹⁷(98-digit number)
15402508430268679838…95449307978597671921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.080 Γ— 10⁹⁷(98-digit number)
30805016860537359677…90898615957195343841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.161 Γ— 10⁹⁷(98-digit number)
61610033721074719355…81797231914390687681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.232 Γ— 10⁹⁸(99-digit number)
12322006744214943871…63594463828781375361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.464 Γ— 10⁹⁸(99-digit number)
24644013488429887742…27188927657562750721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.928 Γ— 10⁹⁸(99-digit number)
49288026976859775484…54377855315125501441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.857 Γ— 10⁹⁸(99-digit number)
98576053953719550969…08755710630251002881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.971 Γ— 10⁹⁹(100-digit number)
19715210790743910193…17511421260502005761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 79141

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 3e2f83cf660fc25f2dc3ef19110ef7e8d1687fece4c3774c306fcace711eba30

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 #79,141 on Chainz β†—
Circulating Supply:57,611,204 XPMΒ·at block #6,795,889 Β· updates every 60s
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