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Block #859,692

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/19/2014, 4:09:26 PM Β· Difficulty 10.9651 Β· 5,964,788 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2123a492bd512e021937f930ff6bdd1a8e8df1b85057aa3a53be6e697bdda84
View on Chainz β†—

Height

#859,692

Difficulty

10.965072

Transactions

1

Size

206 B

Version

2

Bits

0af70ef0

Nonce

2,859,043,449

Timestamp

12/19/2014, 4:09:26 PM

Confirmations

5,964,788

Merkle Root

6bc3db3be363665ada4dc3837cacb500a1f1c32adaad1f3d4fd07ec336be2908
Transactions (1)
Coinbase6bc3db3be36366…d07ec336be2908
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.

4.449 Γ— 10⁹⁴(95-digit number)
44494855332901260982…72085814754801251600
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
4.449 Γ— 10⁹⁴(95-digit number)
44494855332901260982…72085814754801251601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.898 Γ— 10⁹⁴(95-digit number)
88989710665802521964…44171629509602503201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.779 Γ— 10⁹⁡(96-digit number)
17797942133160504392…88343259019205006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.559 Γ— 10⁹⁡(96-digit number)
35595884266321008785…76686518038410012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.119 Γ— 10⁹⁡(96-digit number)
71191768532642017571…53373036076820025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.423 Γ— 10⁹⁢(97-digit number)
14238353706528403514…06746072153640051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.847 Γ— 10⁹⁢(97-digit number)
28476707413056807028…13492144307280102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.695 Γ— 10⁹⁢(97-digit number)
56953414826113614057…26984288614560204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.139 Γ— 10⁹⁷(98-digit number)
11390682965222722811…53968577229120409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.278 Γ— 10⁹⁷(98-digit number)
22781365930445445622…07937154458240819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.556 Γ— 10⁹⁷(98-digit number)
45562731860890891245…15874308916481638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
9.112 Γ— 10⁹⁷(98-digit number)
91125463721781782491…31748617832963276801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 859692

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 d2123a492bd512e021937f930ff6bdd1a8e8df1b85057aa3a53be6e697bdda84

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 #859,692 on Chainz β†—
Circulating Supply:57,839,911 XPMΒ·at block #6,824,479 Β· updates every 60s
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