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Block #857,960

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/18/2014, 5:45:17 AM Β· Difficulty 10.9672 Β· 5,983,934 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5886d5db919768aabefb856125cf6a1fc36a6cab365ac6368aecf9e9d3bdf13c
View on Chainz β†—

Height

#857,960

Difficulty

10.967245

Transactions

1

Size

207 B

Version

2

Bits

0af79d56

Nonce

583,281,465

Timestamp

12/18/2014, 5:45:17 AM

Confirmations

5,983,934

Merkle Root

07f09d86c25c8753dfb8014ed7aa39f37bfa9a45138d259f32ccb9bb86273010
Transactions (1)
Coinbase07f09d86c25c87…ccb9bb86273010
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.630 Γ— 10⁹⁢(97-digit number)
36303083550084957869…15676373215907944960
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
3.630 Γ— 10⁹⁢(97-digit number)
36303083550084957869…15676373215907944961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.260 Γ— 10⁹⁢(97-digit number)
72606167100169915739…31352746431815889921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.452 Γ— 10⁹⁷(98-digit number)
14521233420033983147…62705492863631779841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.904 Γ— 10⁹⁷(98-digit number)
29042466840067966295…25410985727263559681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.808 Γ— 10⁹⁷(98-digit number)
58084933680135932591…50821971454527119361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.161 Γ— 10⁹⁸(99-digit number)
11616986736027186518…01643942909054238721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.323 Γ— 10⁹⁸(99-digit number)
23233973472054373036…03287885818108477441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.646 Γ— 10⁹⁸(99-digit number)
46467946944108746073…06575771636216954881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.293 Γ— 10⁹⁸(99-digit number)
92935893888217492146…13151543272433909761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.858 Γ— 10⁹⁹(100-digit number)
18587178777643498429…26303086544867819521
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 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
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 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 857960

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 5886d5db919768aabefb856125cf6a1fc36a6cab365ac6368aecf9e9d3bdf13c

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 #857,960 on Chainz β†—
Circulating Supply:57,979,528 XPMΒ·at block #6,841,893 Β· updates every 60s
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