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Block #163,576

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 2:11:51 AM Β· Difficulty 9.8621 Β· 6,660,906 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7a657922d7d098a7ec0062983c426426913fd5a7c4628a0dfd1c49ec7f7fbd2e
View on Chainz β†—

Height

#163,576

Difficulty

9.862103

Transactions

1

Size

199 B

Version

2

Bits

09dcb2cc

Nonce

250,121

Timestamp

9/14/2013, 2:11:51 AM

Confirmations

6,660,906

Merkle Root

3eecd2e5ae920370926de104edc7f995683560e00413a7c4396ec9c8c0c780f5
Transactions (1)
Coinbase3eecd2e5ae9203…6ec9c8c0c780f5
1 in β†’ 1 out10.2700 XPM109 B
AHD4Aoxy…173V1iQW
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.

2.220 Γ— 10⁹³(94-digit number)
22203831582169828227…35224097643781504500
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
2.220 Γ— 10⁹³(94-digit number)
22203831582169828227…35224097643781504499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.440 Γ— 10⁹³(94-digit number)
44407663164339656455…70448195287563008999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.881 Γ— 10⁹³(94-digit number)
88815326328679312911…40896390575126017999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.776 Γ— 10⁹⁴(95-digit number)
17763065265735862582…81792781150252035999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.552 Γ— 10⁹⁴(95-digit number)
35526130531471725164…63585562300504071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.105 Γ— 10⁹⁴(95-digit number)
71052261062943450329…27171124601008143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.421 Γ— 10⁹⁡(96-digit number)
14210452212588690065…54342249202016287999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.842 Γ— 10⁹⁡(96-digit number)
28420904425177380131…08684498404032575999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.684 Γ— 10⁹⁡(96-digit number)
56841808850354760263…17368996808065151999
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 163576

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 7a657922d7d098a7ec0062983c426426913fd5a7c4628a0dfd1c49ec7f7fbd2e

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 #163,576 on Chainz β†—
Circulating Supply:57,839,926 XPMΒ·at block #6,824,481 Β· updates every 60s
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