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Home/Chain Registry/Block #2,648,709

Block #2,648,709

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 5:03:58 PM Β· Difficulty 11.7665 Β· 4,187,881 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
88684e1b11b0b5375e4ceb16dc880364e0602c680f38a98dc1d6f4d1d82faaa0
View on Chainz β†—

Difficulty

11.766512

Transactions

2

Size

720 B

Version

2

Bits

0bc43a27

Nonce

204,219,737

Timestamp

5/4/2018, 5:03:58 PM

Confirmations

4,187,881

Merkle Root

2342784195ef305692885b96645549ef50173a09beaf13cc8dda045f0b06a72b
Transactions (2)
Coinbase8af36cd9329f27…e6ea6531e96525
1 in β†’ 1 out7.2200 XPM110 B
AaR1iBi2…iuptTA8N
dd7efe33856148…fa183afe18441e
3 in β†’ 2 out1.0107 XPM521 B
AaLvfwYn…haxTfxUyAS6Ppdm1…CUe6E23P
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.

1.962 Γ— 10⁹³(94-digit number)
19623625838261092487…33192442280827396460
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
1.962 Γ— 10⁹³(94-digit number)
19623625838261092487…33192442280827396459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.924 Γ— 10⁹³(94-digit number)
39247251676522184975…66384884561654792919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.849 Γ— 10⁹³(94-digit number)
78494503353044369950…32769769123309585839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.569 Γ— 10⁹⁴(95-digit number)
15698900670608873990…65539538246619171679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.139 Γ— 10⁹⁴(95-digit number)
31397801341217747980…31079076493238343359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.279 Γ— 10⁹⁴(95-digit number)
62795602682435495960…62158152986476686719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.255 Γ— 10⁹⁡(96-digit number)
12559120536487099192…24316305972953373439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.511 Γ— 10⁹⁡(96-digit number)
25118241072974198384…48632611945906746879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.023 Γ— 10⁹⁡(96-digit number)
50236482145948396768…97265223891813493759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.004 Γ— 10⁹⁢(97-digit number)
10047296429189679353…94530447783626987519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.009 Γ— 10⁹⁢(97-digit number)
20094592858379358707…89060895567253975039
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 2648709

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 88684e1b11b0b5375e4ceb16dc880364e0602c680f38a98dc1d6f4d1d82faaa0

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 #2,648,709 on Chainz β†—
Circulating Supply:57,936,989 XPMΒ·at block #6,836,589 Β· updates every 60s
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