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Block #563,106

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2014, 5:33:53 PM Β· Difficulty 10.9648 Β· 6,235,545 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
694ad9b3495fc1ea3f74ff40fd2265418c78081c88b6c63875f52bc293766f08
View on Chainz β†—

Height

#563,106

Difficulty

10.964764

Transactions

1

Size

208 B

Version

2

Bits

0af6face

Nonce

201,282,890

Timestamp

5/26/2014, 5:33:53 PM

Confirmations

6,235,545

Merkle Root

8447c06020b95b1d3c485f214cb319d9fa56544e9d85830ae0df2f7b1bc42cc0
Transactions (1)
Coinbase8447c06020b95b…df2f7b1bc42cc0
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.

3.248 Γ— 10⁹⁹(100-digit number)
32482189701937299452…55539784656588236800
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
3.248 Γ— 10⁹⁹(100-digit number)
32482189701937299452…55539784656588236801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.496 Γ— 10⁹⁹(100-digit number)
64964379403874598904…11079569313176473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.299 Γ— 10¹⁰⁰(101-digit number)
12992875880774919780…22159138626352947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.598 Γ— 10¹⁰⁰(101-digit number)
25985751761549839561…44318277252705894401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.197 Γ— 10¹⁰⁰(101-digit number)
51971503523099679123…88636554505411788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.039 Γ— 10¹⁰¹(102-digit number)
10394300704619935824…77273109010823577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.078 Γ— 10¹⁰¹(102-digit number)
20788601409239871649…54546218021647155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.157 Γ— 10¹⁰¹(102-digit number)
41577202818479743298…09092436043294310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.315 Γ— 10¹⁰¹(102-digit number)
83154405636959486597…18184872086588620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.663 Γ— 10¹⁰²(103-digit number)
16630881127391897319…36369744173177241601
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 563106

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 694ad9b3495fc1ea3f74ff40fd2265418c78081c88b6c63875f52bc293766f08

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 #563,106 on Chainz β†—
Circulating Supply:57,633,231 XPMΒ·at block #6,798,650 Β· updates every 60s
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