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Block #2,618,407

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/17/2018, 7:04:15 PM Β· Difficulty 11.2391 Β· 4,224,776 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6a935f88234ddcfed92f32be4c61adde28c3d33a3ffa615cd7b9a05eb11fb5b9
View on Chainz β†—

Difficulty

11.239139

Transactions

1

Size

201 B

Version

2

Bits

0b3d382f

Nonce

576,170,967

Timestamp

4/17/2018, 7:04:15 PM

Confirmations

4,224,776

Merkle Root

9d65c6d1556cd007b9c6c8895bf987508be8e227d029b5d9630c00fecc8f323c
Transactions (1)
Coinbase9d65c6d1556cd0…0c00fecc8f323c
1 in β†’ 1 out7.9000 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.

2.790 Γ— 10⁹⁢(97-digit number)
27900534902147046333…94297775852874301440
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
2.790 Γ— 10⁹⁢(97-digit number)
27900534902147046333…94297775852874301439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.580 Γ— 10⁹⁢(97-digit number)
55801069804294092667…88595551705748602879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.116 Γ— 10⁹⁷(98-digit number)
11160213960858818533…77191103411497205759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.232 Γ— 10⁹⁷(98-digit number)
22320427921717637067…54382206822994411519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.464 Γ— 10⁹⁷(98-digit number)
44640855843435274134…08764413645988823039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.928 Γ— 10⁹⁷(98-digit number)
89281711686870548268…17528827291977646079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.785 Γ— 10⁹⁸(99-digit number)
17856342337374109653…35057654583955292159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.571 Γ— 10⁹⁸(99-digit number)
35712684674748219307…70115309167910584319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.142 Γ— 10⁹⁸(99-digit number)
71425369349496438614…40230618335821168639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.428 Γ— 10⁹⁹(100-digit number)
14285073869899287722…80461236671642337279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.857 Γ— 10⁹⁹(100-digit number)
28570147739798575445…60922473343284674559
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 2618407

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 6a935f88234ddcfed92f32be4c61adde28c3d33a3ffa615cd7b9a05eb11fb5b9

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 #2,618,407 on Chainz β†—
Circulating Supply:57,989,832 XPMΒ·at block #6,843,182 Β· updates every 60s
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