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Block #168,209

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2013, 3:48:56 AM Β· Difficulty 9.8681 Β· 6,658,448 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa619f4889a2598311225dfd7274e192b88ff6d7ad4c5f9a4d2d452deec82834
View on Chainz β†—

Height

#168,209

Difficulty

9.868090

Transactions

1

Size

202 B

Version

2

Bits

09de3b1e

Nonce

1,857

Timestamp

9/17/2013, 3:48:56 AM

Confirmations

6,658,448

Merkle Root

03a4749fc1b742c39dcf642506e790c5ab5f9975104e80c6aca4f59910a53601
Transactions (1)
Coinbase03a4749fc1b742…a4f59910a53601
1 in β†’ 1 out10.2500 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.

1.124 Γ— 10⁹⁡(96-digit number)
11243779350210564391…66694206883538211010
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
1.124 Γ— 10⁹⁡(96-digit number)
11243779350210564391…66694206883538211009
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.248 Γ— 10⁹⁡(96-digit number)
22487558700421128783…33388413767076422019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.497 Γ— 10⁹⁡(96-digit number)
44975117400842257566…66776827534152844039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.995 Γ— 10⁹⁡(96-digit number)
89950234801684515133…33553655068305688079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.799 Γ— 10⁹⁢(97-digit number)
17990046960336903026…67107310136611376159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.598 Γ— 10⁹⁢(97-digit number)
35980093920673806053…34214620273222752319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.196 Γ— 10⁹⁢(97-digit number)
71960187841347612106…68429240546445504639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.439 Γ— 10⁹⁷(98-digit number)
14392037568269522421…36858481092891009279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.878 Γ— 10⁹⁷(98-digit number)
28784075136539044842…73716962185782018559
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 168209

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 aa619f4889a2598311225dfd7274e192b88ff6d7ad4c5f9a4d2d452deec82834

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 #168,209 on Chainz β†—
Circulating Supply:57,857,406 XPMΒ·at block #6,826,656 Β· updates every 60s
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