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Block #105,560

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2013, 2:12:28 PM Β· Difficulty 9.5871 Β· 6,720,024 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f617679697c6b682766b5a8eff0e4e056c84ac6b8a869b90785cf6ea0c302c67
View on Chainz β†—

Height

#105,560

Difficulty

9.587090

Transactions

1

Size

205 B

Version

2

Bits

09964b90

Nonce

478,977

Timestamp

8/8/2013, 2:12:28 PM

Confirmations

6,720,024

Merkle Root

7a9fe35ff960b2070b76cf900ed48f3b524b22836ee77c9d5aedd9aaf093321c
Transactions (1)
Coinbase7a9fe35ff960b2…edd9aaf093321c
1 in β†’ 1 out10.8600 XPM112 B
AT5A2KL6…CT16n6i2
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.

7.856 Γ— 10¹⁰¹(102-digit number)
78569118615956279440…45147478980463147920
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
7.856 Γ— 10¹⁰¹(102-digit number)
78569118615956279440…45147478980463147921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.571 Γ— 10¹⁰²(103-digit number)
15713823723191255888…90294957960926295841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.142 Γ— 10¹⁰²(103-digit number)
31427647446382511776…80589915921852591681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.285 Γ— 10¹⁰²(103-digit number)
62855294892765023552…61179831843705183361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.257 Γ— 10¹⁰³(104-digit number)
12571058978553004710…22359663687410366721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.514 Γ— 10¹⁰³(104-digit number)
25142117957106009421…44719327374820733441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.028 Γ— 10¹⁰³(104-digit number)
50284235914212018842…89438654749641466881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.005 Γ— 10¹⁰⁴(105-digit number)
10056847182842403768…78877309499282933761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.011 Γ— 10¹⁰⁴(105-digit number)
20113694365684807536…57754618998565867521
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 105560

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 f617679697c6b682766b5a8eff0e4e056c84ac6b8a869b90785cf6ea0c302c67

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 #105,560 on Chainz β†—
Circulating Supply:57,848,771 XPMΒ·at block #6,825,583 Β· updates every 60s
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