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Block #477,620

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/6/2014, 1:43:07 PM Β· Difficulty 10.4861 Β· 6,318,481 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6f12afd7bc4a831da6c4be1db13ccef2735c79042073e36cf90518ea4f259cd1
View on Chainz β†—

Height

#477,620

Difficulty

10.486102

Transactions

1

Size

208 B

Version

2

Bits

0a7c7129

Nonce

10,072

Timestamp

4/6/2014, 1:43:07 PM

Confirmations

6,318,481

Merkle Root

4af49fd2133a52c6df942de0481ad77427ece491ab815cb1532dadb395b8c1b3
Transactions (1)
Coinbase4af49fd2133a52…2dadb395b8c1b3
1 in β†’ 1 out9.0800 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.

5.434 Γ— 10⁹⁸(99-digit number)
54346752988439434351…30998871885785708560
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
5.434 Γ— 10⁹⁸(99-digit number)
54346752988439434351…30998871885785708561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.086 Γ— 10⁹⁹(100-digit number)
10869350597687886870…61997743771571417121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.173 Γ— 10⁹⁹(100-digit number)
21738701195375773740…23995487543142834241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.347 Γ— 10⁹⁹(100-digit number)
43477402390751547481…47990975086285668481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.695 Γ— 10⁹⁹(100-digit number)
86954804781503094962…95981950172571336961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.739 Γ— 10¹⁰⁰(101-digit number)
17390960956300618992…91963900345142673921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.478 Γ— 10¹⁰⁰(101-digit number)
34781921912601237985…83927800690285347841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.956 Γ— 10¹⁰⁰(101-digit number)
69563843825202475970…67855601380570695681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.391 Γ— 10¹⁰¹(102-digit number)
13912768765040495194…35711202761141391361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.782 Γ— 10¹⁰¹(102-digit number)
27825537530080990388…71422405522282782721
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 477620

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 6f12afd7bc4a831da6c4be1db13ccef2735c79042073e36cf90518ea4f259cd1

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 #477,620 on Chainz β†—
Circulating Supply:57,612,801 XPMΒ·at block #6,796,100 Β· updates every 60s
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