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Block #638,526

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2014, 2:31:36 PM Β· Difficulty 10.9615 Β· 6,187,975 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3375c3b07ff40e3b2d2fafb45356c767dd1a6165b95bfd510989fb76e612e1a8
View on Chainz β†—

Height

#638,526

Difficulty

10.961490

Transactions

1

Size

206 B

Version

2

Bits

0af6243a

Nonce

1,406,293,730

Timestamp

7/18/2014, 2:31:36 PM

Confirmations

6,187,975

Merkle Root

5d68ee4cc04475a0ab841366c7e8d12105661c7fb10e6f4c2201a32ba03053d1
Transactions (1)
Coinbase5d68ee4cc04475…01a32ba03053d1
1 in β†’ 1 out8.3100 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.

2.740 Γ— 10⁹⁡(96-digit number)
27402204388027640346…96801305104641727920
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
2.740 Γ— 10⁹⁡(96-digit number)
27402204388027640346…96801305104641727921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.480 Γ— 10⁹⁡(96-digit number)
54804408776055280693…93602610209283455841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.096 Γ— 10⁹⁢(97-digit number)
10960881755211056138…87205220418566911681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.192 Γ— 10⁹⁢(97-digit number)
21921763510422112277…74410440837133823361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.384 Γ— 10⁹⁢(97-digit number)
43843527020844224554…48820881674267646721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.768 Γ— 10⁹⁢(97-digit number)
87687054041688449109…97641763348535293441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.753 Γ— 10⁹⁷(98-digit number)
17537410808337689821…95283526697070586881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.507 Γ— 10⁹⁷(98-digit number)
35074821616675379643…90567053394141173761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.014 Γ— 10⁹⁷(98-digit number)
70149643233350759287…81134106788282347521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.402 Γ— 10⁹⁸(99-digit number)
14029928646670151857…62268213576564695041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.805 Γ— 10⁹⁸(99-digit number)
28059857293340303715…24536427153129390081
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 638526

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 3375c3b07ff40e3b2d2fafb45356c767dd1a6165b95bfd510989fb76e612e1a8

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 #638,526 on Chainz β†—
Circulating Supply:57,856,150 XPMΒ·at block #6,826,500 Β· updates every 60s
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