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Block #301,441

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/9/2013, 4:55:21 AM Β· Difficulty 9.9925 Β· 6,493,273 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bf5d075d2a7bbdb32a967b1ae0d9a2fe5dd10363cab739ec43ef94c6bdc18262
View on Chainz β†—

Height

#301,441

Difficulty

9.992525

Transactions

1

Size

207 B

Version

2

Bits

09fe161d

Nonce

123,936

Timestamp

12/9/2013, 4:55:21 AM

Confirmations

6,493,273

Merkle Root

c9befda46a192fe290fda59c7252a84043cd6b4e8223baf6bb001c216f275d0f
Transactions (1)
Coinbasec9befda46a192f…001c216f275d0f
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

2.045 Γ— 10⁹⁷(98-digit number)
20453329208229191652…78896456573506328800
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.045 Γ— 10⁹⁷(98-digit number)
20453329208229191652…78896456573506328801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.090 Γ— 10⁹⁷(98-digit number)
40906658416458383304…57792913147012657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.181 Γ— 10⁹⁷(98-digit number)
81813316832916766608…15585826294025315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.636 Γ— 10⁹⁸(99-digit number)
16362663366583353321…31171652588050630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.272 Γ— 10⁹⁸(99-digit number)
32725326733166706643…62343305176101260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.545 Γ— 10⁹⁸(99-digit number)
65450653466333413286…24686610352202521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.309 Γ— 10⁹⁹(100-digit number)
13090130693266682657…49373220704405043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.618 Γ— 10⁹⁹(100-digit number)
26180261386533365314…98746441408810086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.236 Γ— 10⁹⁹(100-digit number)
52360522773066730629…97492882817620172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.047 Γ— 10¹⁰⁰(101-digit number)
10472104554613346125…94985765635240345601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 301441

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 bf5d075d2a7bbdb32a967b1ae0d9a2fe5dd10363cab739ec43ef94c6bdc18262

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 #301,441 on Chainz β†—
Circulating Supply:57,601,760 XPMΒ·at block #6,794,713 Β· updates every 60s
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