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Block #168,217

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2013, 3:57:41 AM Β· Difficulty 9.8681 Β· 6,648,001 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7b43d81fa5500a896ab7861734f696d24635c10a425c2d28f81c66062f0a4711
View on Chainz β†—

Height

#168,217

Difficulty

9.868069

Transactions

1

Size

199 B

Version

2

Bits

09de39c3

Nonce

34,236

Timestamp

9/17/2013, 3:57:41 AM

Confirmations

6,648,001

Merkle Root

237ff39e58d5baaa5631efa3bb716934ef6eba0c2fe7041b0f6f8b3103203e09
Transactions (1)
Coinbase237ff39e58d5ba…6f8b3103203e09
1 in β†’ 1 out10.2500 XPM109 B
ASiN1vnG…nPBYx4TC
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.

3.480 Γ— 10⁹⁴(95-digit number)
34805629701477203030…37328675442594609600
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.480 Γ— 10⁹⁴(95-digit number)
34805629701477203030…37328675442594609599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.961 Γ— 10⁹⁴(95-digit number)
69611259402954406060…74657350885189219199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁡(96-digit number)
13922251880590881212…49314701770378438399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.784 Γ— 10⁹⁡(96-digit number)
27844503761181762424…98629403540756876799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.568 Γ— 10⁹⁡(96-digit number)
55689007522363524848…97258807081513753599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁢(97-digit number)
11137801504472704969…94517614163027507199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.227 Γ— 10⁹⁢(97-digit number)
22275603008945409939…89035228326055014399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.455 Γ— 10⁹⁢(97-digit number)
44551206017890819879…78070456652110028799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.910 Γ— 10⁹⁢(97-digit number)
89102412035781639758…56140913304220057599
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 168217

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 7b43d81fa5500a896ab7861734f696d24635c10a425c2d28f81c66062f0a4711

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 #168,217 on Chainz β†—
Circulating Supply:57,773,873 XPMΒ·at block #6,816,217 Β· updates every 60s
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