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Block #857,791

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/18/2014, 2:43:54 AM Β· Difficulty 10.9673 Β· 5,986,149 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8ab10f0d40158bf01a0afa6e77804f6d241996bc21883c445963ff3d9d3416f6
View on Chainz β†—

Height

#857,791

Difficulty

10.967322

Transactions

2

Size

433 B

Version

2

Bits

0af7a26f

Nonce

190,907,979

Timestamp

12/18/2014, 2:43:54 AM

Confirmations

5,986,149

Merkle Root

a8c39d158b885eb89ab7ed5592d1f1b08ff49196a0d510ce7d3a579caa7f097a
Transactions (2)
Coinbase976e7592edd243…ba1101fe40c0fc
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
561b45b8770a31…57638d57084328
1 in β†’ 2 out0.0394 XPM226 B
AMMpedMg…j3Pxz8L4AKt1mRvs…Ajvxzi4t
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.

2.519 Γ— 10⁹⁢(97-digit number)
25192798613956691564…76985561036079987200
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
2.519 Γ— 10⁹⁢(97-digit number)
25192798613956691564…76985561036079987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.038 Γ— 10⁹⁢(97-digit number)
50385597227913383128…53971122072159974399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.007 Γ— 10⁹⁷(98-digit number)
10077119445582676625…07942244144319948799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.015 Γ— 10⁹⁷(98-digit number)
20154238891165353251…15884488288639897599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.030 Γ— 10⁹⁷(98-digit number)
40308477782330706502…31768976577279795199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.061 Γ— 10⁹⁷(98-digit number)
80616955564661413005…63537953154559590399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁸(99-digit number)
16123391112932282601…27075906309119180799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.224 Γ— 10⁹⁸(99-digit number)
32246782225864565202…54151812618238361599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.449 Γ— 10⁹⁸(99-digit number)
64493564451729130404…08303625236476723199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.289 Γ— 10⁹⁹(100-digit number)
12898712890345826080…16607250472953446399
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 857791

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 8ab10f0d40158bf01a0afa6e77804f6d241996bc21883c445963ff3d9d3416f6

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 #857,791 on Chainz β†—
Circulating Supply:57,995,896 XPMΒ·at block #6,843,939 Β· updates every 60s
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