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Home/Chain Registry/Block #837,144

Block #837,144

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2014, 3:09:36 PM Β· Difficulty 10.9759 Β· 6,004,932 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4b193dbf0c0074c5426f132a3717c82d6c01167e04c644140caee7334540819b
View on Chainz β†—

Height

#837,144

Difficulty

10.975904

Transactions

1

Size

207 B

Version

2

Bits

0af9d4d9

Nonce

734,088,300

Timestamp

12/2/2014, 3:09:36 PM

Confirmations

6,004,932

Merkle Root

7b1a8cfa58dd3344b263e93c3df365d298c1a1a1bf86d4a6d881712b54d5f4dc
Transactions (1)
Coinbase7b1a8cfa58dd33…81712b54d5f4dc
1 in β†’ 1 out8.2900 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.

2.692 Γ— 10⁹⁷(98-digit number)
26921299945397865030…58652817396208025600
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
2.692 Γ— 10⁹⁷(98-digit number)
26921299945397865030…58652817396208025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.384 Γ— 10⁹⁷(98-digit number)
53842599890795730061…17305634792416051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.076 Γ— 10⁹⁸(99-digit number)
10768519978159146012…34611269584832102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.153 Γ— 10⁹⁸(99-digit number)
21537039956318292024…69222539169664204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.307 Γ— 10⁹⁸(99-digit number)
43074079912636584049…38445078339328409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.614 Γ— 10⁹⁸(99-digit number)
86148159825273168098…76890156678656819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.722 Γ— 10⁹⁹(100-digit number)
17229631965054633619…53780313357313638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.445 Γ— 10⁹⁹(100-digit number)
34459263930109267239…07560626714627276801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.891 Γ— 10⁹⁹(100-digit number)
68918527860218534479…15121253429254553601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.378 Γ— 10¹⁰⁰(101-digit number)
13783705572043706895…30242506858509107201
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 837144

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 4b193dbf0c0074c5426f132a3717c82d6c01167e04c644140caee7334540819b

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 #837,144 on Chainz β†—
Circulating Supply:57,980,993 XPMΒ·at block #6,842,075 Β· updates every 60s
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