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Block #479,681

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/7/2014, 8:11:25 PM Β· Difficulty 10.5098 Β· 6,345,793 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
06d56e1a27bde9dba4acd0b46c2a91c3770a5ed31c8c3fd83b481a4a8fb1634b
View on Chainz β†—

Height

#479,681

Difficulty

10.509833

Transactions

1

Size

207 B

Version

2

Bits

0a82846d

Nonce

275,476,660

Timestamp

4/7/2014, 8:11:25 PM

Confirmations

6,345,793

Merkle Root

e53d470c4897e9d3c86b8c2feb9bac18c67cb6915a1a33e3db0a3a21f786efd5
Transactions (1)
Coinbasee53d470c4897e9…0a3a21f786efd5
1 in β†’ 1 out9.0400 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.

2.010 Γ— 10⁹⁷(98-digit number)
20103219080466922121…21464417646224857080
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
2.010 Γ— 10⁹⁷(98-digit number)
20103219080466922121…21464417646224857081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.020 Γ— 10⁹⁷(98-digit number)
40206438160933844242…42928835292449714161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.041 Γ— 10⁹⁷(98-digit number)
80412876321867688484…85857670584899428321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.608 Γ— 10⁹⁸(99-digit number)
16082575264373537696…71715341169798856641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.216 Γ— 10⁹⁸(99-digit number)
32165150528747075393…43430682339597713281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.433 Γ— 10⁹⁸(99-digit number)
64330301057494150787…86861364679195426561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.286 Γ— 10⁹⁹(100-digit number)
12866060211498830157…73722729358390853121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.573 Γ— 10⁹⁹(100-digit number)
25732120422997660315…47445458716781706241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.146 Γ— 10⁹⁹(100-digit number)
51464240845995320630…94890917433563412481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.029 Γ— 10¹⁰⁰(101-digit number)
10292848169199064126…89781834867126824961
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 479681

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 06d56e1a27bde9dba4acd0b46c2a91c3770a5ed31c8c3fd83b481a4a8fb1634b

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 #479,681 on Chainz β†—
Circulating Supply:57,847,885 XPMΒ·at block #6,825,473 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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