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Block #854,805

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/15/2014, 9:39:00 PM Β· Difficulty 10.9685 Β· 5,946,008 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
327bee4101b962e02ac046a962069a4f0d8a6dd8e3dfea7e0fbb4755f4f64d13
View on Chainz β†—

Height

#854,805

Difficulty

10.968509

Transactions

2

Size

583 B

Version

2

Bits

0af7f03b

Nonce

591,559,830

Timestamp

12/15/2014, 9:39:00 PM

Confirmations

5,946,008

Merkle Root

895dad3be3abbd006f47d6008f4bee22ae805e3d3f26aaa85ed0f8955a818f4a
Transactions (2)
Coinbase918c8cfab225b8…eea8f5daefec9d
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
e111d11218f0a8…371d6d8adddafd
2 in β†’ 2 out11.1906 XPM376 B
AeZd3bQP…mZ35TWE9AUY54LT9…Q8pWMHVG
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.

4.493 Γ— 10⁹⁢(97-digit number)
44938471986785285087…99807740132899967040
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
4.493 Γ— 10⁹⁢(97-digit number)
44938471986785285087…99807740132899967041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.987 Γ— 10⁹⁢(97-digit number)
89876943973570570175…99615480265799934081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.797 Γ— 10⁹⁷(98-digit number)
17975388794714114035…99230960531599868161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.595 Γ— 10⁹⁷(98-digit number)
35950777589428228070…98461921063199736321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.190 Γ— 10⁹⁷(98-digit number)
71901555178856456140…96923842126399472641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.438 Γ— 10⁹⁸(99-digit number)
14380311035771291228…93847684252798945281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.876 Γ— 10⁹⁸(99-digit number)
28760622071542582456…87695368505597890561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.752 Γ— 10⁹⁸(99-digit number)
57521244143085164912…75390737011195781121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.150 Γ— 10⁹⁹(100-digit number)
11504248828617032982…50781474022391562241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.300 Γ— 10⁹⁹(100-digit number)
23008497657234065964…01562948044783124481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.601 Γ— 10⁹⁹(100-digit number)
46016995314468131929…03125896089566248961
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 854805

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 327bee4101b962e02ac046a962069a4f0d8a6dd8e3dfea7e0fbb4755f4f64d13

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 #854,805 on Chainz β†—
Circulating Supply:57,650,559 XPMΒ·at block #6,800,812 Β· updates every 60s
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