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Block #295,201

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2013, 7:38:18 AM Β· Difficulty 9.9913 Β· 6,505,195 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f351b4ded25c5ade993701c69ad46f83a875236544add0d93f971c7202ce455d
View on Chainz β†—

Height

#295,201

Difficulty

9.991292

Transactions

1

Size

208 B

Version

2

Bits

09fdc54d

Nonce

36,256

Timestamp

12/5/2013, 7:38:18 AM

Confirmations

6,505,195

Merkle Root

24a920033039a1d9e5fe9b4d6e48412b579d747dcab6d827314d19921faa76d7
Transactions (1)
Coinbase24a920033039a1…4d19921faa76d7
1 in β†’ 1 out10.0000 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.

5.787 Γ— 10⁹⁹(100-digit number)
57873350111734610509…26274455251750081750
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
5.787 Γ— 10⁹⁹(100-digit number)
57873350111734610509…26274455251750081749
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.157 Γ— 10¹⁰⁰(101-digit number)
11574670022346922101…52548910503500163499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.314 Γ— 10¹⁰⁰(101-digit number)
23149340044693844203…05097821007000326999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.629 Γ— 10¹⁰⁰(101-digit number)
46298680089387688407…10195642014000653999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.259 Γ— 10¹⁰⁰(101-digit number)
92597360178775376814…20391284028001307999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.851 Γ— 10¹⁰¹(102-digit number)
18519472035755075362…40782568056002615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.703 Γ— 10¹⁰¹(102-digit number)
37038944071510150725…81565136112005231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.407 Γ— 10¹⁰¹(102-digit number)
74077888143020301451…63130272224010463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.481 Γ— 10¹⁰²(103-digit number)
14815577628604060290…26260544448020927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.963 Γ— 10¹⁰²(103-digit number)
29631155257208120580…52521088896041855999
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 295201

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 f351b4ded25c5ade993701c69ad46f83a875236544add0d93f971c7202ce455d

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 #295,201 on Chainz β†—
Circulating Supply:57,647,229 XPMΒ·at block #6,800,395 Β· updates every 60s
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