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Block #475,442

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/5/2014, 6:00:12 AM Β· Difficulty 10.4565 Β· 6,325,561 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0cffe21905d81c8bc698b769b2409518d25f6b011ae348fe0da11239eb3ec172
View on Chainz β†—

Height

#475,442

Difficulty

10.456532

Transactions

1

Size

202 B

Version

2

Bits

0a74df4a

Nonce

77,810

Timestamp

4/5/2014, 6:00:12 AM

Confirmations

6,325,561

Merkle Root

daf842b35cde443dfc37364478cd54e886d33480d073a9a0f6ce70cff5cc5b6e
Transactions (1)
Coinbasedaf842b35cde44…ce70cff5cc5b6e
1 in β†’ 1 out9.1300 XPM110 B
AR6arNiM…HUa2VqVg
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.

1.153 Γ— 10¹⁰⁰(101-digit number)
11539924356892501770…66793383443849825280
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
1.153 Γ— 10¹⁰⁰(101-digit number)
11539924356892501770…66793383443849825281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.307 Γ— 10¹⁰⁰(101-digit number)
23079848713785003541…33586766887699650561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.615 Γ— 10¹⁰⁰(101-digit number)
46159697427570007082…67173533775399301121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.231 Γ— 10¹⁰⁰(101-digit number)
92319394855140014164…34347067550798602241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.846 Γ— 10¹⁰¹(102-digit number)
18463878971028002832…68694135101597204481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.692 Γ— 10¹⁰¹(102-digit number)
36927757942056005665…37388270203194408961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.385 Γ— 10¹⁰¹(102-digit number)
73855515884112011331…74776540406388817921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.477 Γ— 10¹⁰²(103-digit number)
14771103176822402266…49553080812777635841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.954 Γ— 10¹⁰²(103-digit number)
29542206353644804532…99106161625555271681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.908 Γ— 10¹⁰²(103-digit number)
59084412707289609065…98212323251110543361
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 475442

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 0cffe21905d81c8bc698b769b2409518d25f6b011ae348fe0da11239eb3ec172

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 #475,442 on Chainz β†—
Circulating Supply:57,652,083 XPMΒ·at block #6,801,002 Β· updates every 60s
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