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Block #840,535

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/5/2014, 5:44:22 AM Β· Difficulty 10.9742 Β· 5,986,781 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37c187ccf879d5e89d6341c5db6fa2eafe6d49ed3e9ab060e7f7dd4dd5bd89e4
View on Chainz β†—

Height

#840,535

Difficulty

10.974207

Transactions

1

Size

207 B

Version

2

Bits

0af965a2

Nonce

2,647,721,219

Timestamp

12/5/2014, 5:44:22 AM

Confirmations

5,986,781

Merkle Root

559c3e060f0787c638944ebbca0d6eb44bf3f72e9dcfd2b5d50dab06118c36be
Transactions (1)
Coinbase559c3e060f0787…0dab06118c36be
1 in β†’ 1 out8.2900 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.

1.064 Γ— 10⁹⁢(97-digit number)
10645265461282232411…22988753055689942400
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
1.064 Γ— 10⁹⁢(97-digit number)
10645265461282232411…22988753055689942401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.129 Γ— 10⁹⁢(97-digit number)
21290530922564464823…45977506111379884801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.258 Γ— 10⁹⁢(97-digit number)
42581061845128929646…91955012222759769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.516 Γ— 10⁹⁢(97-digit number)
85162123690257859292…83910024445519539201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.703 Γ— 10⁹⁷(98-digit number)
17032424738051571858…67820048891039078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.406 Γ— 10⁹⁷(98-digit number)
34064849476103143716…35640097782078156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.812 Γ— 10⁹⁷(98-digit number)
68129698952206287433…71280195564156313601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.362 Γ— 10⁹⁸(99-digit number)
13625939790441257486…42560391128312627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.725 Γ— 10⁹⁸(99-digit number)
27251879580882514973…85120782256625254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.450 Γ— 10⁹⁸(99-digit number)
54503759161765029947…70241564513250508801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.090 Γ— 10⁹⁹(100-digit number)
10900751832353005989…40483129026501017601
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 840535

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 37c187ccf879d5e89d6341c5db6fa2eafe6d49ed3e9ab060e7f7dd4dd5bd89e4

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 #840,535 on Chainz β†—
Circulating Supply:57,862,641 XPMΒ·at block #6,827,315 Β· updates every 60s
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