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Block #256,329

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/11/2013, 6:34:16 PM Β· Difficulty 9.9752 Β· 6,545,142 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
207c2b32c7722c50006d4e31327ab2afd8215a443f20cc0b0d8fbdae95d0cb7d
View on Chainz β†—

Height

#256,329

Difficulty

9.975167

Transactions

1

Size

232 B

Version

2

Bits

09f9a48c

Nonce

471

Timestamp

11/11/2013, 6:34:16 PM

Confirmations

6,545,142

Merkle Root

3af6b606c4ac16ce2650dd2d762e63b09eb2b81e8b0f0ae7c5cb177c6a36a1c2
Transactions (1)
Coinbase3af6b606c4ac16…cb177c6a36a1c2
1 in β†’ 2 out10.0300 XPM142 B
AKcbk49N…GJbKa7j1AHsw4d6U…EnM8UXNZ
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.

2.501 Γ— 10⁹⁴(95-digit number)
25015414739562865819…12868088794511741300
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
2.501 Γ— 10⁹⁴(95-digit number)
25015414739562865819…12868088794511741299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.003 Γ— 10⁹⁴(95-digit number)
50030829479125731638…25736177589023482599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.000 Γ— 10⁹⁡(96-digit number)
10006165895825146327…51472355178046965199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.001 Γ— 10⁹⁡(96-digit number)
20012331791650292655…02944710356093930399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.002 Γ— 10⁹⁡(96-digit number)
40024663583300585311…05889420712187860799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.004 Γ— 10⁹⁡(96-digit number)
80049327166601170622…11778841424375721599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.600 Γ— 10⁹⁢(97-digit number)
16009865433320234124…23557682848751443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.201 Γ— 10⁹⁢(97-digit number)
32019730866640468248…47115365697502886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.403 Γ— 10⁹⁢(97-digit number)
64039461733280936497…94230731395005772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.280 Γ— 10⁹⁷(98-digit number)
12807892346656187299…88461462790011545599
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 256329

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 207c2b32c7722c50006d4e31327ab2afd8215a443f20cc0b0d8fbdae95d0cb7d

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 #256,329 on Chainz β†—
Circulating Supply:57,655,844 XPMΒ·at block #6,801,470 Β· updates every 60s
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