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Block #194,897

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/5/2013, 10:30:33 AM Β· Difficulty 9.8802 Β· 6,629,608 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
00e74f1ceedfa3127f80e35cd15d809a56cf7843d4283ec9871ba566cb1d2b4b
View on Chainz β†—

Height

#194,897

Difficulty

9.880233

Transactions

1

Size

205 B

Version

2

Bits

09e156fb

Nonce

50,336,597

Timestamp

10/5/2013, 10:30:33 AM

Confirmations

6,629,608

Merkle Root

b7df0c348a371730c93e919ece3195e0115ba6139b069b925888aba2a0b036db
Transactions (1)
Coinbaseb7df0c348a3717…88aba2a0b036db
1 in β†’ 1 out10.2300 XPM116 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.

3.351 Γ— 10⁹¹(92-digit number)
33511036958970373143…49507295880271493120
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
3.351 Γ— 10⁹¹(92-digit number)
33511036958970373143…49507295880271493119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.702 Γ— 10⁹¹(92-digit number)
67022073917940746287…99014591760542986239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.340 Γ— 10⁹²(93-digit number)
13404414783588149257…98029183521085972479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.680 Γ— 10⁹²(93-digit number)
26808829567176298515…96058367042171944959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.361 Γ— 10⁹²(93-digit number)
53617659134352597030…92116734084343889919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.072 Γ— 10⁹³(94-digit number)
10723531826870519406…84233468168687779839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.144 Γ— 10⁹³(94-digit number)
21447063653741038812…68466936337375559679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.289 Γ— 10⁹³(94-digit number)
42894127307482077624…36933872674751119359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.578 Γ— 10⁹³(94-digit number)
85788254614964155248…73867745349502238719
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 194897

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 00e74f1ceedfa3127f80e35cd15d809a56cf7843d4283ec9871ba566cb1d2b4b

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 #194,897 on Chainz β†—
Circulating Supply:57,840,100 XPMΒ·at block #6,824,504 Β· updates every 60s
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