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Home/Chain Registry/Block #2,648,707

Block #2,648,707

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 5:01:34 PM Β· Difficulty 11.7665 Β· 4,187,746 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
626f1759bca81a3ddf1550b4a203f758bfec971ef6a73dec10f46795722f6674
View on Chainz β†—

Difficulty

11.766523

Transactions

1

Size

200 B

Version

2

Bits

0bc43adc

Nonce

955,527,831

Timestamp

5/4/2018, 5:01:34 PM

Confirmations

4,187,746

Merkle Root

d2a69f5128e696a044b596a435af267a108c63a6f158de03bbcd06065cb1def9
Transactions (1)
Coinbased2a69f5128e696…cd06065cb1def9
1 in β†’ 1 out7.2100 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.258 Γ— 10⁹⁡(96-digit number)
12584272953817884996…30421888725436200960
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
1.258 Γ— 10⁹⁡(96-digit number)
12584272953817884996…30421888725436200959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.516 Γ— 10⁹⁡(96-digit number)
25168545907635769993…60843777450872401919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.033 Γ— 10⁹⁡(96-digit number)
50337091815271539986…21687554901744803839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.006 Γ— 10⁹⁢(97-digit number)
10067418363054307997…43375109803489607679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.013 Γ— 10⁹⁢(97-digit number)
20134836726108615994…86750219606979215359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.026 Γ— 10⁹⁢(97-digit number)
40269673452217231989…73500439213958430719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.053 Γ— 10⁹⁢(97-digit number)
80539346904434463978…47000878427916861439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.610 Γ— 10⁹⁷(98-digit number)
16107869380886892795…94001756855833722879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.221 Γ— 10⁹⁷(98-digit number)
32215738761773785591…88003513711667445759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.443 Γ— 10⁹⁷(98-digit number)
64431477523547571182…76007027423334891519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.288 Γ— 10⁹⁸(99-digit number)
12886295504709514236…52014054846669783039
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 2648707

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 626f1759bca81a3ddf1550b4a203f758bfec971ef6a73dec10f46795722f6674

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 #2,648,707 on Chainz β†—
Circulating Supply:57,935,895 XPMΒ·at block #6,836,452 Β· updates every 60s
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