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Block #462,236

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/27/2014, 7:56:09 AM Β· Difficulty 10.4084 Β· 6,353,590 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
99564f9f9c9a5799e11baf4d16bf1075e53ab461432f62b856e18bd6ece99896
View on Chainz β†—

Height

#462,236

Difficulty

10.408444

Transactions

1

Size

187 B

Version

2

Bits

0a688fd0

Nonce

556,750

Timestamp

3/27/2014, 7:56:09 AM

Confirmations

6,353,590

Merkle Root

19422cd869023111da2ac821f32648cb8b39158e0eee7ae65646120b298796d6
Transactions (1)
Coinbase19422cd8690231…46120b298796d6
1 in β†’ 1 out9.2200 XPM97 B
ANEZwy9t…E1uf5dKY
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.

7.436 Γ— 10⁹⁴(95-digit number)
74369854303293795244…70636765251201911040
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
7.436 Γ— 10⁹⁴(95-digit number)
74369854303293795244…70636765251201911041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.487 Γ— 10⁹⁡(96-digit number)
14873970860658759048…41273530502403822081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.974 Γ— 10⁹⁡(96-digit number)
29747941721317518097…82547061004807644161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.949 Γ— 10⁹⁡(96-digit number)
59495883442635036195…65094122009615288321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.189 Γ— 10⁹⁢(97-digit number)
11899176688527007239…30188244019230576641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.379 Γ— 10⁹⁢(97-digit number)
23798353377054014478…60376488038461153281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.759 Γ— 10⁹⁢(97-digit number)
47596706754108028956…20752976076922306561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.519 Γ— 10⁹⁢(97-digit number)
95193413508216057913…41505952153844613121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.903 Γ— 10⁹⁷(98-digit number)
19038682701643211582…83011904307689226241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.807 Γ— 10⁹⁷(98-digit number)
38077365403286423165…66023808615378452481
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 462236

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 99564f9f9c9a5799e11baf4d16bf1075e53ab461432f62b856e18bd6ece99896

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 #462,236 on Chainz β†—
Circulating Supply:57,770,717 XPMΒ·at block #6,815,825 Β· updates every 60s
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