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Block #299,194

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/7/2013, 7:46:10 PM Β· Difficulty 9.9921 Β· 6,500,862 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6ba8a869ccd75ba7c84942999a5d18aefa60329f335192bce1246f7b18ab1dd4
View on Chainz β†—

Height

#299,194

Difficulty

9.992062

Transactions

1

Size

199 B

Version

2

Bits

09fdf7bf

Nonce

82,239

Timestamp

12/7/2013, 7:46:10 PM

Confirmations

6,500,862

Merkle Root

b21a76150e458c815227fe56ad43d9c7c7dce90adcfa15583bdb1de8e047068a
Transactions (1)
Coinbaseb21a76150e458c…db1de8e047068a
1 in β†’ 1 out10.0000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.077 Γ— 10⁹²(93-digit number)
30779156804201469467…16971424422560601040
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
3.077 Γ— 10⁹²(93-digit number)
30779156804201469467…16971424422560601039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.155 Γ— 10⁹²(93-digit number)
61558313608402938935…33942848845121202079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.231 Γ— 10⁹³(94-digit number)
12311662721680587787…67885697690242404159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.462 Γ— 10⁹³(94-digit number)
24623325443361175574…35771395380484808319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.924 Γ— 10⁹³(94-digit number)
49246650886722351148…71542790760969616639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.849 Γ— 10⁹³(94-digit number)
98493301773444702296…43085581521939233279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.969 Γ— 10⁹⁴(95-digit number)
19698660354688940459…86171163043878466559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.939 Γ— 10⁹⁴(95-digit number)
39397320709377880918…72342326087756933119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.879 Γ— 10⁹⁴(95-digit number)
78794641418755761837…44684652175513866239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.575 Γ— 10⁹⁡(96-digit number)
15758928283751152367…89369304351027732479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 299194

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 6ba8a869ccd75ba7c84942999a5d18aefa60329f335192bce1246f7b18ab1dd4

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 #299,194 on Chainz β†—
Circulating Supply:57,644,509 XPMΒ·at block #6,800,055 Β· updates every 60s
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