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Block #195,836

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/6/2013, 2:11:25 AM Β· Difficulty 9.8804 Β· 6,599,820 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8c31df4ec3b11f8be4bc5d74c31b0e2235873b5ebedd1fbea413723e4662ccda
View on Chainz β†—

Height

#195,836

Difficulty

9.880435

Transactions

1

Size

200 B

Version

2

Bits

09e16437

Nonce

30,164

Timestamp

10/6/2013, 2:11:25 AM

Confirmations

6,599,820

Merkle Root

d929664cc2065508de8a26f1f782d9a9cf8cc2e2811160acc371b37decec27b0
Transactions (1)
Coinbased929664cc20655…71b37decec27b0
1 in β†’ 1 out10.2300 XPM109 B
ATBixbiv…QmpHjijf
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.

2.642 Γ— 10⁹⁢(97-digit number)
26420276055178329921…30355369225713164800
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
2.642 Γ— 10⁹⁢(97-digit number)
26420276055178329921…30355369225713164799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.284 Γ— 10⁹⁢(97-digit number)
52840552110356659843…60710738451426329599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.056 Γ— 10⁹⁷(98-digit number)
10568110422071331968…21421476902852659199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.113 Γ— 10⁹⁷(98-digit number)
21136220844142663937…42842953805705318399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.227 Γ— 10⁹⁷(98-digit number)
42272441688285327874…85685907611410636799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.454 Γ— 10⁹⁷(98-digit number)
84544883376570655749…71371815222821273599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.690 Γ— 10⁹⁸(99-digit number)
16908976675314131149…42743630445642547199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.381 Γ— 10⁹⁸(99-digit number)
33817953350628262299…85487260891285094399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.763 Γ— 10⁹⁸(99-digit number)
67635906701256524599…70974521782570188799
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 195836

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 8c31df4ec3b11f8be4bc5d74c31b0e2235873b5ebedd1fbea413723e4662ccda

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 #195,836 on Chainz β†—
Circulating Supply:57,609,320 XPMΒ·at block #6,795,655 Β· updates every 60s
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