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Block #840,780

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2014, 9:46:43 AM Β· Difficulty 10.9742 Β· 5,999,963 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dbf7b14ebffa56e432416ef92e594380eb0bfd499063e07764965858630d7155
View on Chainz β†—

Height

#840,780

Difficulty

10.974230

Transactions

2

Size

433 B

Version

2

Bits

0af9671c

Nonce

1,192,256,008

Timestamp

12/5/2014, 9:46:43 AM

Confirmations

5,999,963

Merkle Root

1896d95fb63258a0e3780ad6a4454c9b950f4d0b97e16736bde95b4fdf75f0db
Transactions (2)
Coinbase23364370e1314f…36f881a9a61451
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
98d097fa1acac6…d27c2cb4f376c0
1 in β†’ 2 out0.3817 XPM226 B
AQccZmvv…3SBrqxsvAcA6nvHw…bPFdan5t
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.

1.605 Γ— 10⁹⁢(97-digit number)
16053194423218971100…72952729074828621600
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
1.605 Γ— 10⁹⁢(97-digit number)
16053194423218971100…72952729074828621599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.210 Γ— 10⁹⁢(97-digit number)
32106388846437942200…45905458149657243199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.421 Γ— 10⁹⁢(97-digit number)
64212777692875884401…91810916299314486399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.284 Γ— 10⁹⁷(98-digit number)
12842555538575176880…83621832598628972799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.568 Γ— 10⁹⁷(98-digit number)
25685111077150353760…67243665197257945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.137 Γ— 10⁹⁷(98-digit number)
51370222154300707521…34487330394515891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.027 Γ— 10⁹⁸(99-digit number)
10274044430860141504…68974660789031782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.054 Γ— 10⁹⁸(99-digit number)
20548088861720283008…37949321578063564799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.109 Γ— 10⁹⁸(99-digit number)
41096177723440566017…75898643156127129599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.219 Γ— 10⁹⁸(99-digit number)
82192355446881132034…51797286312254259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.643 Γ— 10⁹⁹(100-digit number)
16438471089376226406…03594572624508518399
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 840780

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 dbf7b14ebffa56e432416ef92e594380eb0bfd499063e07764965858630d7155

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 #840,780 on Chainz β†—
Circulating Supply:57,970,287 XPMΒ·at block #6,840,742 Β· updates every 60s
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