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Home/Chain Registry/Block #2,647,828

Block #2,647,828

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 3:40:13 AM Β· Difficulty 11.7628 Β· 4,185,252 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c1bebfbeef724fe2564e224c441286d562ef39066725824f979794162508b637
View on Chainz β†—

Difficulty

11.762811

Transactions

1

Size

200 B

Version

2

Bits

0bc34790

Nonce

454,086,467

Timestamp

5/4/2018, 3:40:13 AM

Confirmations

4,185,252

Merkle Root

2956187454758d92d91a30d2336aaa03442165019fff59ff22b36160d646246f
Transactions (1)
Coinbase2956187454758d…b36160d646246f
1 in β†’ 1 out7.2200 XPM110 B
ASBW3VyW…Df1KX87o
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.

2.065 Γ— 10⁹⁡(96-digit number)
20650003684847792177…52493488018683512000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.065 Γ— 10⁹⁡(96-digit number)
20650003684847792177…52493488018683511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.130 Γ— 10⁹⁡(96-digit number)
41300007369695584354…04986976037367023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.260 Γ— 10⁹⁡(96-digit number)
82600014739391168709…09973952074734047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.652 Γ— 10⁹⁢(97-digit number)
16520002947878233741…19947904149468095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.304 Γ— 10⁹⁢(97-digit number)
33040005895756467483…39895808298936191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.608 Γ— 10⁹⁢(97-digit number)
66080011791512934967…79791616597872383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.321 Γ— 10⁹⁷(98-digit number)
13216002358302586993…59583233195744767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.643 Γ— 10⁹⁷(98-digit number)
26432004716605173986…19166466391489535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.286 Γ— 10⁹⁷(98-digit number)
52864009433210347973…38332932782979071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.057 Γ— 10⁹⁸(99-digit number)
10572801886642069594…76665865565958143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.114 Γ— 10⁹⁸(99-digit number)
21145603773284139189…53331731131916287999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2647828

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 c1bebfbeef724fe2564e224c441286d562ef39066725824f979794162508b637

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 #2,647,828 on Chainz β†—
Circulating Supply:57,908,813 XPMΒ·at block #6,833,079 Β· updates every 60s
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