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Block #79,899

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/23/2013, 7:51:18 PM Β· Difficulty 9.2416 Β· 6,737,926 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e23956fdbf2a9d3b2eb73cb44bcf3fecbd3a573a6a1eb06839e4b19aa6553186
View on Chainz β†—

Height

#79,899

Difficulty

9.241569

Transactions

1

Size

202 B

Version

2

Bits

093dd777

Nonce

41,656

Timestamp

7/23/2013, 7:51:18 PM

Confirmations

6,737,926

Merkle Root

ebe9d3800c54cf75e3da66aa3f0bf0edb75b2aad101329e34d0a034f36031a4c
Transactions (1)
Coinbaseebe9d3800c54cf…0a034f36031a4c
1 in β†’ 1 out11.6900 XPM109 B
AHndoX1F…U1Rfa5uk
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.

6.447 Γ— 10¹⁰¹(102-digit number)
64473391783275014197…59752206956741921840
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
6.447 Γ— 10¹⁰¹(102-digit number)
64473391783275014197…59752206956741921841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.289 Γ— 10¹⁰²(103-digit number)
12894678356655002839…19504413913483843681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.578 Γ— 10¹⁰²(103-digit number)
25789356713310005678…39008827826967687361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.157 Γ— 10¹⁰²(103-digit number)
51578713426620011357…78017655653935374721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.031 Γ— 10¹⁰³(104-digit number)
10315742685324002271…56035311307870749441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.063 Γ— 10¹⁰³(104-digit number)
20631485370648004543…12070622615741498881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.126 Γ— 10¹⁰³(104-digit number)
41262970741296009086…24141245231482997761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.252 Γ— 10¹⁰³(104-digit number)
82525941482592018172…48282490462965995521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.650 Γ— 10¹⁰⁴(105-digit number)
16505188296518403634…96564980925931991041
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 79899

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 e23956fdbf2a9d3b2eb73cb44bcf3fecbd3a573a6a1eb06839e4b19aa6553186

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 #79,899 on Chainz β†—
Circulating Supply:57,786,664 XPMΒ·at block #6,817,824 Β· updates every 60s
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