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Block #576,515

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2014, 3:40:58 PM Β· Difficulty 10.9689 Β· 6,240,343 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0bf1665b211f77228074bbd33e5ef15a2199e99ae00cdd26a2ae1f52adcf2da7
View on Chainz β†—

Height

#576,515

Difficulty

10.968852

Transactions

1

Size

208 B

Version

2

Bits

0af806a7

Nonce

490,615,620

Timestamp

6/4/2014, 3:40:58 PM

Confirmations

6,240,343

Merkle Root

24635984a6f782111aef70d549d2ce2c600f01aa174443b8c64f6cf90719d992
Transactions (1)
Coinbase24635984a6f782…4f6cf90719d992
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

9.441 Γ— 10⁹⁹(100-digit number)
94410452612151291241…41203957110638540800
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
9.441 Γ— 10⁹⁹(100-digit number)
94410452612151291241…41203957110638540801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.888 Γ— 10¹⁰⁰(101-digit number)
18882090522430258248…82407914221277081601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.776 Γ— 10¹⁰⁰(101-digit number)
37764181044860516496…64815828442554163201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.552 Γ— 10¹⁰⁰(101-digit number)
75528362089721032993…29631656885108326401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.510 Γ— 10¹⁰¹(102-digit number)
15105672417944206598…59263313770216652801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.021 Γ— 10¹⁰¹(102-digit number)
30211344835888413197…18526627540433305601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.042 Γ— 10¹⁰¹(102-digit number)
60422689671776826394…37053255080866611201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.208 Γ— 10¹⁰²(103-digit number)
12084537934355365278…74106510161733222401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.416 Γ— 10¹⁰²(103-digit number)
24169075868710730557…48213020323466444801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.833 Γ— 10¹⁰²(103-digit number)
48338151737421461115…96426040646932889601
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 576515

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 0bf1665b211f77228074bbd33e5ef15a2199e99ae00cdd26a2ae1f52adcf2da7

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 #576,515 on Chainz β†—
Circulating Supply:57,778,907 XPMΒ·at block #6,816,857 Β· updates every 60s
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