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Block #879,438

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/2/2015, 4:34:26 PM Β· Difficulty 10.9625 Β· 5,951,415 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0523f13f879501857d25f10f937a2cef0f8e92ae6baf30b8d2fb282c34ca1d1d
View on Chainz β†—

Height

#879,438

Difficulty

10.962516

Transactions

1

Size

207 B

Version

2

Bits

0af6677b

Nonce

763,030,279

Timestamp

1/2/2015, 4:34:26 PM

Confirmations

5,951,415

Merkle Root

c7b15a28f9a9a431d2f6dc1f1226b67dedd0c9f1919e11d50ea2b1b52ac351a0
Transactions (1)
Coinbasec7b15a28f9a9a4…a2b1b52ac351a0
1 in β†’ 1 out8.3100 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.

6.741 Γ— 10⁹⁷(98-digit number)
67414093824639843500…99388441872865290240
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
6.741 Γ— 10⁹⁷(98-digit number)
67414093824639843500…99388441872865290241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.348 Γ— 10⁹⁸(99-digit number)
13482818764927968700…98776883745730580481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.696 Γ— 10⁹⁸(99-digit number)
26965637529855937400…97553767491461160961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.393 Γ— 10⁹⁸(99-digit number)
53931275059711874800…95107534982922321921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.078 Γ— 10⁹⁹(100-digit number)
10786255011942374960…90215069965844643841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.157 Γ— 10⁹⁹(100-digit number)
21572510023884749920…80430139931689287681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.314 Γ— 10⁹⁹(100-digit number)
43145020047769499840…60860279863378575361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.629 Γ— 10⁹⁹(100-digit number)
86290040095538999680…21720559726757150721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.725 Γ— 10¹⁰⁰(101-digit number)
17258008019107799936…43441119453514301441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.451 Γ— 10¹⁰⁰(101-digit number)
34516016038215599872…86882238907028602881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.903 Γ— 10¹⁰⁰(101-digit number)
69032032076431199744…73764477814057205761
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 879438

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 0523f13f879501857d25f10f937a2cef0f8e92ae6baf30b8d2fb282c34ca1d1d

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 #879,438 on Chainz β†—
Circulating Supply:57,890,959 XPMΒ·at block #6,830,852 Β· updates every 60s
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