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Block #193,906

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/4/2013, 7:24:38 PM Β· Difficulty 9.8779 Β· 6,649,352 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c32fb2289569fb69232c810c22122f7010b1a7e1eaf9246748601c571c0969bd
View on Chainz β†—

Height

#193,906

Difficulty

9.877912

Transactions

1

Size

207 B

Version

2

Bits

09e0bed6

Nonce

2,796

Timestamp

10/4/2013, 7:24:38 PM

Confirmations

6,649,352

Merkle Root

092e42a2cc85522416052ba28b8dabdb6a73a90716eeeb2de8e68dd4d6f4a8fc
Transactions (1)
Coinbase092e42a2cc8552…e68dd4d6f4a8fc
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.

3.536 Γ— 10⁹⁷(98-digit number)
35361470351680102059…86219442826027045800
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
3.536 Γ— 10⁹⁷(98-digit number)
35361470351680102059…86219442826027045799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.072 Γ— 10⁹⁷(98-digit number)
70722940703360204119…72438885652054091599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.414 Γ— 10⁹⁸(99-digit number)
14144588140672040823…44877771304108183199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.828 Γ— 10⁹⁸(99-digit number)
28289176281344081647…89755542608216366399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.657 Γ— 10⁹⁸(99-digit number)
56578352562688163295…79511085216432732799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.131 Γ— 10⁹⁹(100-digit number)
11315670512537632659…59022170432865465599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.263 Γ— 10⁹⁹(100-digit number)
22631341025075265318…18044340865730931199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.526 Γ— 10⁹⁹(100-digit number)
45262682050150530636…36088681731461862399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.052 Γ— 10⁹⁹(100-digit number)
90525364100301061272…72177363462923724799
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 193906

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 c32fb2289569fb69232c810c22122f7010b1a7e1eaf9246748601c571c0969bd

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 #193,906 on Chainz β†—
Circulating Supply:57,990,437 XPMΒ·at block #6,843,257 Β· updates every 60s
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