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Home/Chain Registry/Block #2,647,673

Block #2,647,673

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 1:37:39 AM Β· Difficulty 11.7613 Β· 4,191,855 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
648e2faa8b6c25838aea37f7c05c1f00d057a0407bfabf6814fe1cc418d9407d
View on Chainz β†—

Difficulty

11.761297

Transactions

2

Size

721 B

Version

2

Bits

0bc2e456

Nonce

1,157,507,568

Timestamp

5/4/2018, 1:37:39 AM

Confirmations

4,191,855

Merkle Root

956b8f364b66713e3d606fb04bb25bb8544815718c5f269eed36013992af6b30
Transactions (2)
Coinbaseeccf7e9b0c9943…e788c475dda1ec
1 in β†’ 1 out7.2300 XPM110 B
AKfBajHj…Jezh67ja
54215394422c7d…8c98e3feb9fa02
3 in β†’ 2 out184.4451 XPM521 B
ANxpdD4J…aUiJjKvpAaCt2Z2e…QB2Doko7
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.

8.270 Γ— 10⁹⁴(95-digit number)
82705102817044327819…66144858326082793600
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
8.270 Γ— 10⁹⁴(95-digit number)
82705102817044327819…66144858326082793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.654 Γ— 10⁹⁡(96-digit number)
16541020563408865563…32289716652165587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.308 Γ— 10⁹⁡(96-digit number)
33082041126817731127…64579433304331174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.616 Γ— 10⁹⁡(96-digit number)
66164082253635462255…29158866608662348799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.323 Γ— 10⁹⁢(97-digit number)
13232816450727092451…58317733217324697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.646 Γ— 10⁹⁢(97-digit number)
26465632901454184902…16635466434649395199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.293 Γ— 10⁹⁢(97-digit number)
52931265802908369804…33270932869298790399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.058 Γ— 10⁹⁷(98-digit number)
10586253160581673960…66541865738597580799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.117 Γ— 10⁹⁷(98-digit number)
21172506321163347921…33083731477195161599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.234 Γ— 10⁹⁷(98-digit number)
42345012642326695843…66167462954390323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.469 Γ— 10⁹⁷(98-digit number)
84690025284653391686…32334925908780646399
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 2647673

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 648e2faa8b6c25838aea37f7c05c1f00d057a0407bfabf6814fe1cc418d9407d

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 #2,647,673 on Chainz β†—
Circulating Supply:57,960,524 XPMΒ·at block #6,839,527 Β· updates every 60s
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