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Block #2,854,620

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/25/2018, 1:36:13 PM Β· Difficulty 11.7077 Β· 3,989,259 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
83b383b1906993a416aaa94dce360d4737c66a3d74baf389c9a4597b670eb6c3
View on Chainz β†—

Difficulty

11.707744

Transactions

1

Size

201 B

Version

2

Bits

0bb52eb9

Nonce

1,331,789,685

Timestamp

9/25/2018, 1:36:13 PM

Confirmations

3,989,259

Merkle Root

d7baf2e1850115e5b4188763b139587c9ac1d9ab4d5e62699095a478dfe5c762
Transactions (1)
Coinbased7baf2e1850115…95a478dfe5c762
1 in β†’ 1 out7.2800 XPM110 B
AYa9DR9S…nDqqyK4d
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.

2.306 Γ— 10⁹⁷(98-digit number)
23067672536059944869…06080783320109566720
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.306 Γ— 10⁹⁷(98-digit number)
23067672536059944869…06080783320109566721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.613 Γ— 10⁹⁷(98-digit number)
46135345072119889738…12161566640219133441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.227 Γ— 10⁹⁷(98-digit number)
92270690144239779476…24323133280438266881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.845 Γ— 10⁹⁸(99-digit number)
18454138028847955895…48646266560876533761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.690 Γ— 10⁹⁸(99-digit number)
36908276057695911790…97292533121753067521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.381 Γ— 10⁹⁸(99-digit number)
73816552115391823581…94585066243506135041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.476 Γ— 10⁹⁹(100-digit number)
14763310423078364716…89170132487012270081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.952 Γ— 10⁹⁹(100-digit number)
29526620846156729432…78340264974024540161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.905 Γ— 10⁹⁹(100-digit number)
59053241692313458864…56680529948049080321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.181 Γ— 10¹⁰⁰(101-digit number)
11810648338462691772…13361059896098160641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.362 Γ— 10¹⁰⁰(101-digit number)
23621296676925383545…26722119792196321281
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2854620

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 83b383b1906993a416aaa94dce360d4737c66a3d74baf389c9a4597b670eb6c3

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 #2,854,620 on Chainz β†—
Circulating Supply:57,995,403 XPMΒ·at block #6,843,878 Β· updates every 60s
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