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Block #512,504

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/26/2014, 9:56:20 PM Β· Difficulty 10.8339 Β· 6,283,383 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bf18ea1c748b9c59cd1c47d3626efe416200d9671fec4fa22da498b79043479c
View on Chainz β†—

Height

#512,504

Difficulty

10.833918

Transactions

1

Size

208 B

Version

2

Bits

0ad57ba2

Nonce

73,606,824

Timestamp

4/26/2014, 9:56:20 PM

Confirmations

6,283,383

Merkle Root

f2e975fbb3c025ffdc28cfba8733b26a5c805f99f07ac621fe1203aa4c0d3e51
Transactions (1)
Coinbasef2e975fbb3c025…1203aa4c0d3e51
1 in β†’ 1 out8.5100 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.

3.805 Γ— 10⁹⁸(99-digit number)
38055626530518253046…05939931290748027200
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
3.805 Γ— 10⁹⁸(99-digit number)
38055626530518253046…05939931290748027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.611 Γ— 10⁹⁸(99-digit number)
76111253061036506093…11879862581496054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.522 Γ— 10⁹⁹(100-digit number)
15222250612207301218…23759725162992108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.044 Γ— 10⁹⁹(100-digit number)
30444501224414602437…47519450325984217601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.088 Γ— 10⁹⁹(100-digit number)
60889002448829204874…95038900651968435201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.217 Γ— 10¹⁰⁰(101-digit number)
12177800489765840974…90077801303936870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.435 Γ— 10¹⁰⁰(101-digit number)
24355600979531681949…80155602607873740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.871 Γ— 10¹⁰⁰(101-digit number)
48711201959063363899…60311205215747481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.742 Γ— 10¹⁰⁰(101-digit number)
97422403918126727799…20622410431494963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.948 Γ— 10¹⁰¹(102-digit number)
19484480783625345559…41244820862989926401
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 512504

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 bf18ea1c748b9c59cd1c47d3626efe416200d9671fec4fa22da498b79043479c

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 #512,504 on Chainz β†—
Circulating Supply:57,611,179 XPMΒ·at block #6,795,886 Β· updates every 60s
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