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Block #230,781

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/28/2013, 12:47:33 AM Β· Difficulty 9.9399 Β· 6,613,108 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0d345dcfec7b4322bbca89bb69bd823376f366339f26243b9e3efb5cc237fdb5
View on Chainz β†—

Height

#230,781

Difficulty

9.939939

Transactions

1

Size

207 B

Version

2

Bits

09f09fda

Nonce

5,133

Timestamp

10/28/2013, 12:47:33 AM

Confirmations

6,613,108

Merkle Root

d589ad1d0a981130409f86e8738dfc89b35cf042adb5d6421a066e4077ec9ec0
Transactions (1)
Coinbased589ad1d0a9811…066e4077ec9ec0
1 in β†’ 1 out10.1100 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.

1.558 Γ— 10⁹⁢(97-digit number)
15580845466497670626…78677773673505757120
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
1.558 Γ— 10⁹⁢(97-digit number)
15580845466497670626…78677773673505757119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.116 Γ— 10⁹⁢(97-digit number)
31161690932995341252…57355547347011514239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.232 Γ— 10⁹⁢(97-digit number)
62323381865990682505…14711094694023028479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.246 Γ— 10⁹⁷(98-digit number)
12464676373198136501…29422189388046056959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.492 Γ— 10⁹⁷(98-digit number)
24929352746396273002…58844378776092113919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.985 Γ— 10⁹⁷(98-digit number)
49858705492792546004…17688757552184227839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.971 Γ— 10⁹⁷(98-digit number)
99717410985585092009…35377515104368455679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.994 Γ— 10⁹⁸(99-digit number)
19943482197117018401…70755030208736911359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.988 Γ— 10⁹⁸(99-digit number)
39886964394234036803…41510060417473822719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.977 Γ— 10⁹⁸(99-digit number)
79773928788468073607…83020120834947645439
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 230781

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 0d345dcfec7b4322bbca89bb69bd823376f366339f26243b9e3efb5cc237fdb5

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 #230,781 on Chainz β†—
Circulating Supply:57,995,481 XPMΒ·at block #6,843,888 Β· updates every 60s
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