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Block #252,660

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/9/2013, 5:03:44 PM Β· Difficulty 9.9714 Β· 6,550,544 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
81e9d76a12925143e49a2b7239f3bda920e2a3aa491a22136fa9cefb7886ef5a
View on Chainz β†—

Height

#252,660

Difficulty

9.971363

Transactions

2

Size

424 B

Version

2

Bits

09f8ab40

Nonce

36,875

Timestamp

11/9/2013, 5:03:44 PM

Confirmations

6,550,544

Merkle Root

e9a76192f0ead41724ba524264d1fcf9afbc8735a41ac33fc6dda6d219881361
Transactions (2)
Coinbase6a35abf92e536b…510932f0190b52
1 in β†’ 1 out10.0500 XPM109 B
AYDZhi2A…15tJmJHB
31e4dd086f916f…65019d4abd408b
1 in β†’ 2 out0.4900 XPM226 B
ARjqnoYd…FsP3c6ZDAK4vGUUj…hAGTj45C
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.

2.107 Γ— 10⁹³(94-digit number)
21079252715691196846…46464827750379745280
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
2.107 Γ— 10⁹³(94-digit number)
21079252715691196846…46464827750379745281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.215 Γ— 10⁹³(94-digit number)
42158505431382393692…92929655500759490561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.431 Γ— 10⁹³(94-digit number)
84317010862764787385…85859311001518981121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.686 Γ— 10⁹⁴(95-digit number)
16863402172552957477…71718622003037962241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.372 Γ— 10⁹⁴(95-digit number)
33726804345105914954…43437244006075924481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.745 Γ— 10⁹⁴(95-digit number)
67453608690211829908…86874488012151848961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.349 Γ— 10⁹⁡(96-digit number)
13490721738042365981…73748976024303697921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.698 Γ— 10⁹⁡(96-digit number)
26981443476084731963…47497952048607395841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.396 Γ— 10⁹⁡(96-digit number)
53962886952169463926…94995904097214791681
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 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
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 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 252660

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 81e9d76a12925143e49a2b7239f3bda920e2a3aa491a22136fa9cefb7886ef5a

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 #252,660 on Chainz β†—
Circulating Supply:57,669,654 XPMΒ·at block #6,803,203 Β· updates every 60s
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