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Block #195,729

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/6/2013, 12:26:15 AM Β· Difficulty 9.8803 Β· 6,621,702 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42c1a49f9c01b47170b21b4116a706a52c9d3acf2bd5518db7b2a8bb3a6d120c
View on Chainz β†—

Height

#195,729

Difficulty

9.880330

Transactions

1

Size

206 B

Version

2

Bits

09e15d50

Nonce

806

Timestamp

10/6/2013, 12:26:15 AM

Confirmations

6,621,702

Merkle Root

942fe2ca2caf52e2a535b96d237938f5e9285d28e4f3270ef52ddbc494bd8995
Transactions (1)
Coinbase942fe2ca2caf52…2ddbc494bd8995
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.

5.374 Γ— 10⁹⁴(95-digit number)
53740883354621661546…23394669009756384240
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
5.374 Γ— 10⁹⁴(95-digit number)
53740883354621661546…23394669009756384239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁡(96-digit number)
10748176670924332309…46789338019512768479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁡(96-digit number)
21496353341848664618…93578676039025536959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.299 Γ— 10⁹⁡(96-digit number)
42992706683697329237…87157352078051073919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.598 Γ— 10⁹⁡(96-digit number)
85985413367394658474…74314704156102147839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁢(97-digit number)
17197082673478931694…48629408312204295679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.439 Γ— 10⁹⁢(97-digit number)
34394165346957863389…97258816624408591359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.878 Γ— 10⁹⁢(97-digit number)
68788330693915726779…94517633248817182719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.375 Γ— 10⁹⁷(98-digit number)
13757666138783145355…89035266497634365439
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 195729

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 42c1a49f9c01b47170b21b4116a706a52c9d3acf2bd5518db7b2a8bb3a6d120c

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 #195,729 on Chainz β†—
Circulating Supply:57,783,494 XPMΒ·at block #6,817,430 Β· updates every 60s
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