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Block #309,881

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/13/2013, 7:36:20 PM Β· Difficulty 9.9950 Β· 6,517,316 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
36eedfa5a6c439a11ffdf47e45b578450963ee8c85f893d7cc5d2b764c9b542a
View on Chainz β†—

Height

#309,881

Difficulty

9.994990

Transactions

1

Size

206 B

Version

2

Bits

09feb7a8

Nonce

153,150

Timestamp

12/13/2013, 7:36:20 PM

Confirmations

6,517,316

Merkle Root

3728d9633b35360c3fdd0da76d6bd7ad4adc1c1d9bd6e9c16193493f21ed7d3a
Transactions (1)
Coinbase3728d9633b3536…93493f21ed7d3a
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.

1.725 Γ— 10⁹⁡(96-digit number)
17259837631439801757…87431680496785336320
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
1.725 Γ— 10⁹⁡(96-digit number)
17259837631439801757…87431680496785336321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.451 Γ— 10⁹⁡(96-digit number)
34519675262879603514…74863360993570672641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.903 Γ— 10⁹⁡(96-digit number)
69039350525759207029…49726721987141345281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.380 Γ— 10⁹⁢(97-digit number)
13807870105151841405…99453443974282690561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.761 Γ— 10⁹⁢(97-digit number)
27615740210303682811…98906887948565381121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.523 Γ— 10⁹⁢(97-digit number)
55231480420607365623…97813775897130762241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.104 Γ— 10⁹⁷(98-digit number)
11046296084121473124…95627551794261524481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.209 Γ— 10⁹⁷(98-digit number)
22092592168242946249…91255103588523048961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.418 Γ— 10⁹⁷(98-digit number)
44185184336485892498…82510207177046097921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.837 Γ— 10⁹⁷(98-digit number)
88370368672971784997…65020414354092195841
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 309881

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 36eedfa5a6c439a11ffdf47e45b578450963ee8c85f893d7cc5d2b764c9b542a

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 #309,881 on Chainz β†—
Circulating Supply:57,861,672 XPMΒ·at block #6,827,196 Β· updates every 60s
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