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Block #171,980

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/19/2013, 9:37:12 PM Β· Difficulty 9.8636 Β· 6,628,666 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7ea7907d9760bef1ec32dac4c01fe9fbb5aeaa8af6578b602e0ecf55474d3cfe
View on Chainz β†—

Height

#171,980

Difficulty

9.863608

Transactions

1

Size

202 B

Version

2

Bits

09dd156d

Nonce

50,335,138

Timestamp

9/19/2013, 9:37:12 PM

Confirmations

6,628,666

Merkle Root

ba42a99071508b47d2347d843e21845fe27cff84dfc7fec65896f7f0e251d50e
Transactions (1)
Coinbaseba42a99071508b…96f7f0e251d50e
1 in β†’ 1 out10.2600 XPM112 B
AcLBm5Z9…S683d7c3
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.

4.155 Γ— 10⁹⁡(96-digit number)
41555567375112800043…51753769180709846000
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
4.155 Γ— 10⁹⁡(96-digit number)
41555567375112800043…51753769180709846001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.311 Γ— 10⁹⁡(96-digit number)
83111134750225600086…03507538361419692001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.662 Γ— 10⁹⁢(97-digit number)
16622226950045120017…07015076722839384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.324 Γ— 10⁹⁢(97-digit number)
33244453900090240034…14030153445678768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.648 Γ— 10⁹⁢(97-digit number)
66488907800180480069…28060306891357536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.329 Γ— 10⁹⁷(98-digit number)
13297781560036096013…56120613782715072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.659 Γ— 10⁹⁷(98-digit number)
26595563120072192027…12241227565430144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.319 Γ— 10⁹⁷(98-digit number)
53191126240144384055…24482455130860288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.063 Γ— 10⁹⁸(99-digit number)
10638225248028876811…48964910261720576001
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 171980

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 7ea7907d9760bef1ec32dac4c01fe9fbb5aeaa8af6578b602e0ecf55474d3cfe

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 #171,980 on Chainz β†—
Circulating Supply:57,649,228 XPMΒ·at block #6,800,645 Β· updates every 60s
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