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Block #257,031

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/12/2013, 5:15:15 AM Β· Difficulty 9.9755 Β· 6,558,024 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d3fc64d12ead78ed4be311982bdef7f940d02da2fffb3ef2fc62128ce3c6c503
View on Chainz β†—

Height

#257,031

Difficulty

9.975527

Transactions

1

Size

187 B

Version

2

Bits

09f9bc29

Nonce

54,368

Timestamp

11/12/2013, 5:15:15 AM

Confirmations

6,558,024

Merkle Root

8f2431f4d4a5a2bd1054ebc64a5c5cc19c4ff7519c1df6dedf0d7e8c22190b24
Transactions (1)
Coinbase8f2431f4d4a5a2…0d7e8c22190b24
1 in β†’ 1 out10.0300 XPM97 B
ALFhmsQi…V5bffJmU
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.

9.347 Γ— 10⁹⁴(95-digit number)
93473038851911435523…11835331094011392000
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
9.347 Γ— 10⁹⁴(95-digit number)
93473038851911435523…11835331094011392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.869 Γ— 10⁹⁡(96-digit number)
18694607770382287104…23670662188022784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.738 Γ— 10⁹⁡(96-digit number)
37389215540764574209…47341324376045568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.477 Γ— 10⁹⁡(96-digit number)
74778431081529148418…94682648752091136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.495 Γ— 10⁹⁢(97-digit number)
14955686216305829683…89365297504182272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.991 Γ— 10⁹⁢(97-digit number)
29911372432611659367…78730595008364544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.982 Γ— 10⁹⁢(97-digit number)
59822744865223318735…57461190016729088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.196 Γ— 10⁹⁷(98-digit number)
11964548973044663747…14922380033458176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.392 Γ— 10⁹⁷(98-digit number)
23929097946089327494…29844760066916352001
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 257031

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 d3fc64d12ead78ed4be311982bdef7f940d02da2fffb3ef2fc62128ce3c6c503

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 #257,031 on Chainz β†—
Circulating Supply:57,764,530 XPMΒ·at block #6,815,054 Β· updates every 60s
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