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Block #663,022

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2014, 1:20:28 AM Β· Difficulty 10.9571 Β· 6,150,949 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b1af467b61397ae1e01074ca37aeccc9fec027668d62c3901d17b5a8de67a1df
View on Chainz β†—

Height

#663,022

Difficulty

10.957068

Transactions

1

Size

207 B

Version

2

Bits

0af5026f

Nonce

604,381,248

Timestamp

8/5/2014, 1:20:28 AM

Confirmations

6,150,949

Merkle Root

ca60c9162c2906c2ae24d4ae616b7c121f439fccd6e6358b6b4872d575e30edb
Transactions (1)
Coinbaseca60c9162c2906…4872d575e30edb
1 in β†’ 1 out8.3200 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.

3.204 Γ— 10⁹⁢(97-digit number)
32049626389575606818…12704405003479813120
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
3.204 Γ— 10⁹⁢(97-digit number)
32049626389575606818…12704405003479813121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.409 Γ— 10⁹⁢(97-digit number)
64099252779151213637…25408810006959626241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.281 Γ— 10⁹⁷(98-digit number)
12819850555830242727…50817620013919252481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.563 Γ— 10⁹⁷(98-digit number)
25639701111660485454…01635240027838504961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.127 Γ— 10⁹⁷(98-digit number)
51279402223320970909…03270480055677009921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.025 Γ— 10⁹⁸(99-digit number)
10255880444664194181…06540960111354019841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.051 Γ— 10⁹⁸(99-digit number)
20511760889328388363…13081920222708039681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.102 Γ— 10⁹⁸(99-digit number)
41023521778656776727…26163840445416079361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.204 Γ— 10⁹⁸(99-digit number)
82047043557313553455…52327680890832158721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.640 Γ— 10⁹⁹(100-digit number)
16409408711462710691…04655361781664317441
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 663022

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 b1af467b61397ae1e01074ca37aeccc9fec027668d62c3901d17b5a8de67a1df

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 #663,022 on Chainz β†—
Circulating Supply:57,755,844 XPMΒ·at block #6,813,970 Β· updates every 60s
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