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Block #578,037

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/5/2014, 6:08:28 PM Β· Difficulty 10.9685 Β· 6,225,640 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
db959caf5cb730b00a7e6d8d7cf6fe5b9313e14fc4a1e02bc87ef89e12a59928
View on Chainz β†—

Height

#578,037

Difficulty

10.968493

Transactions

1

Size

208 B

Version

2

Bits

0af7ef2d

Nonce

510,826,621

Timestamp

6/5/2014, 6:08:28 PM

Confirmations

6,225,640

Merkle Root

86d53b44a521d5566cb3d8d19faae75eadb603e8357a32f54325ba0ffe74307f
Transactions (1)
Coinbase86d53b44a521d5…25ba0ffe74307f
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.

8.324 Γ— 10⁹⁸(99-digit number)
83240745436940270898…34736771272832926080
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
8.324 Γ— 10⁹⁸(99-digit number)
83240745436940270898…34736771272832926081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.664 Γ— 10⁹⁹(100-digit number)
16648149087388054179…69473542545665852161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.329 Γ— 10⁹⁹(100-digit number)
33296298174776108359…38947085091331704321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.659 Γ— 10⁹⁹(100-digit number)
66592596349552216718…77894170182663408641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.331 Γ— 10¹⁰⁰(101-digit number)
13318519269910443343…55788340365326817281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.663 Γ— 10¹⁰⁰(101-digit number)
26637038539820886687…11576680730653634561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.327 Γ— 10¹⁰⁰(101-digit number)
53274077079641773375…23153361461307269121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.065 Γ— 10¹⁰¹(102-digit number)
10654815415928354675…46306722922614538241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.130 Γ— 10¹⁰¹(102-digit number)
21309630831856709350…92613445845229076481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.261 Γ— 10¹⁰¹(102-digit number)
42619261663713418700…85226891690458152961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.523 Γ— 10¹⁰¹(102-digit number)
85238523327426837400…70453783380916305921
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 578037

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 db959caf5cb730b00a7e6d8d7cf6fe5b9313e14fc4a1e02bc87ef89e12a59928

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 #578,037 on Chainz β†—
Circulating Supply:57,673,451 XPMΒ·at block #6,803,676 Β· updates every 60s
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