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Block #2,825,483

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2018, 7:07:32 AM Β· Difficulty 11.7097 Β· 4,017,417 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
af1b329be3013924d293c91ebcea97b10808ed9d2b1f2eed3e648884a5e21c5f
View on Chainz β†—

Difficulty

11.709668

Transactions

1

Size

200 B

Version

2

Bits

0bb5acd1

Nonce

998,487,301

Timestamp

9/5/2018, 7:07:32 AM

Confirmations

4,017,417

Merkle Root

ef892fb0b19a9b7a72d8a514dcb4968f5eb521e39697850290d673a0af4d62ee
Transactions (1)
Coinbaseef892fb0b19a9b…d673a0af4d62ee
1 in β†’ 1 out7.2800 XPM110 B
AJ9caBS6…TadatArn
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.

2.315 Γ— 10⁹⁡(96-digit number)
23157056684725124972…90797064354063928320
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
2.315 Γ— 10⁹⁡(96-digit number)
23157056684725124972…90797064354063928319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.631 Γ— 10⁹⁡(96-digit number)
46314113369450249944…81594128708127856639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.262 Γ— 10⁹⁡(96-digit number)
92628226738900499889…63188257416255713279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.852 Γ— 10⁹⁢(97-digit number)
18525645347780099977…26376514832511426559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.705 Γ— 10⁹⁢(97-digit number)
37051290695560199955…52753029665022853119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.410 Γ— 10⁹⁢(97-digit number)
74102581391120399911…05506059330045706239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.482 Γ— 10⁹⁷(98-digit number)
14820516278224079982…11012118660091412479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.964 Γ— 10⁹⁷(98-digit number)
29641032556448159964…22024237320182824959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.928 Γ— 10⁹⁷(98-digit number)
59282065112896319929…44048474640365649919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.185 Γ— 10⁹⁸(99-digit number)
11856413022579263985…88096949280731299839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.371 Γ— 10⁹⁸(99-digit number)
23712826045158527971…76193898561462599679
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 2825483

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 af1b329be3013924d293c91ebcea97b10808ed9d2b1f2eed3e648884a5e21c5f

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 #2,825,483 on Chainz β†—
Circulating Supply:57,987,548 XPMΒ·at block #6,842,899 Β· updates every 60s
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