XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #856,020

Block #856,020

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2014, 6:55:49 PM Β· Difficulty 10.9681 Β· 5,974,904 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
272af62941a2b81ade5158c18c8468f362e6eea25ed57dcd28845a95c421155b
View on Chainz β†—

Height

#856,020

Difficulty

10.968143

Transactions

1

Size

199 B

Version

2

Bits

0af7d840

Nonce

1,875,158,062

Timestamp

12/16/2014, 6:55:49 PM

Confirmations

5,974,904

Merkle Root

caecabce1b841b6c9c6b4cd0b9a73656db368d445b926fbab417140d1efb1989
Transactions (1)
Coinbasecaecabce1b841b…17140d1efb1989
1 in β†’ 1 out8.3000 XPM109 B
ASzk5BEu…gSTBHXvg
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.

1.477 Γ— 10⁹⁴(95-digit number)
14777092964272275559…95713125692483538680
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
1.477 Γ— 10⁹⁴(95-digit number)
14777092964272275559…95713125692483538679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.955 Γ— 10⁹⁴(95-digit number)
29554185928544551119…91426251384967077359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.910 Γ— 10⁹⁴(95-digit number)
59108371857089102238…82852502769934154719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.182 Γ— 10⁹⁡(96-digit number)
11821674371417820447…65705005539868309439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.364 Γ— 10⁹⁡(96-digit number)
23643348742835640895…31410011079736618879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.728 Γ— 10⁹⁡(96-digit number)
47286697485671281790…62820022159473237759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.457 Γ— 10⁹⁡(96-digit number)
94573394971342563581…25640044318946475519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.891 Γ— 10⁹⁢(97-digit number)
18914678994268512716…51280088637892951039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.782 Γ— 10⁹⁢(97-digit number)
37829357988537025432…02560177275785902079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.565 Γ— 10⁹⁢(97-digit number)
75658715977074050865…05120354551571804159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 856020

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 272af62941a2b81ade5158c18c8468f362e6eea25ed57dcd28845a95c421155b

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 #856,020 on Chainz β†—
Circulating Supply:57,891,523 XPMΒ·at block #6,830,923 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy