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Block #295,312

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/5/2013, 9:12:13 AM Β· Difficulty 9.9913 Β· 6,522,615 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0ef4e7f1100f1c5f2ac483daa28e44a2d512a5318650c8a6e60b9613e85b9b95
View on Chainz β†—

Height

#295,312

Difficulty

9.991325

Transactions

1

Size

208 B

Version

2

Bits

09fdc77c

Nonce

4,158

Timestamp

12/5/2013, 9:12:13 AM

Confirmations

6,522,615

Merkle Root

c6d43b9685bac19b53d6f1c95abb7d25a0a543e69574738cc62759fa505d2182
Transactions (1)
Coinbasec6d43b9685bac1…2759fa505d2182
1 in β†’ 1 out10.0000 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.

2.231 Γ— 10¹⁰⁰(101-digit number)
22313071711233559858…47787710365239134720
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
2.231 Γ— 10¹⁰⁰(101-digit number)
22313071711233559858…47787710365239134721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.462 Γ— 10¹⁰⁰(101-digit number)
44626143422467119716…95575420730478269441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.925 Γ— 10¹⁰⁰(101-digit number)
89252286844934239433…91150841460956538881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.785 Γ— 10¹⁰¹(102-digit number)
17850457368986847886…82301682921913077761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.570 Γ— 10¹⁰¹(102-digit number)
35700914737973695773…64603365843826155521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.140 Γ— 10¹⁰¹(102-digit number)
71401829475947391547…29206731687652311041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.428 Γ— 10¹⁰²(103-digit number)
14280365895189478309…58413463375304622081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.856 Γ— 10¹⁰²(103-digit number)
28560731790378956618…16826926750609244161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.712 Γ— 10¹⁰²(103-digit number)
57121463580757913237…33653853501218488321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.142 Γ— 10¹⁰³(104-digit number)
11424292716151582647…67307707002436976641
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 295312

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 0ef4e7f1100f1c5f2ac483daa28e44a2d512a5318650c8a6e60b9613e85b9b95

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 #295,312 on Chainz β†—
Circulating Supply:57,787,483 XPMΒ·at block #6,817,926 Β· updates every 60s
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