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Block #352,167

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/10/2014, 4:20:53 AM Β· Difficulty 10.3033 Β· 6,448,638 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e3dbc7d1fdca4e8d8e436482903d992816885b7bb485ae352fd4af6ef94ddc32
View on Chainz β†—

Height

#352,167

Difficulty

10.303348

Transactions

1

Size

207 B

Version

2

Bits

0a4da83a

Nonce

5,482

Timestamp

1/10/2014, 4:20:53 AM

Confirmations

6,448,638

Merkle Root

c29fca954e9d0861ec47335766fcd301d35e368ef3ab68127b353d44ee1b96c6
Transactions (1)
Coinbasec29fca954e9d08…353d44ee1b96c6
1 in β†’ 1 out9.4100 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.

4.896 Γ— 10⁹⁷(98-digit number)
48969316297494005499…20087019328378512000
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
4.896 Γ— 10⁹⁷(98-digit number)
48969316297494005499…20087019328378512001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.793 Γ— 10⁹⁷(98-digit number)
97938632594988010998…40174038656757024001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.958 Γ— 10⁹⁸(99-digit number)
19587726518997602199…80348077313514048001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.917 Γ— 10⁹⁸(99-digit number)
39175453037995204399…60696154627028096001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.835 Γ— 10⁹⁸(99-digit number)
78350906075990408798…21392309254056192001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.567 Γ— 10⁹⁹(100-digit number)
15670181215198081759…42784618508112384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.134 Γ— 10⁹⁹(100-digit number)
31340362430396163519…85569237016224768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.268 Γ— 10⁹⁹(100-digit number)
62680724860792327038…71138474032449536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.253 Γ— 10¹⁰⁰(101-digit number)
12536144972158465407…42276948064899072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.507 Γ— 10¹⁰⁰(101-digit number)
25072289944316930815…84553896129798144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.014 Γ— 10¹⁰⁰(101-digit number)
50144579888633861631…69107792259596288001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 352167

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 e3dbc7d1fdca4e8d8e436482903d992816885b7bb485ae352fd4af6ef94ddc32

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 #352,167 on Chainz β†—
Circulating Supply:57,650,493 XPMΒ·at block #6,800,804 Β· updates every 60s
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