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Block #285,053

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/30/2013, 8:49:25 AM Β· Difficulty 9.9837 Β· 6,557,430 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
75714c5ff9a0bf485e674d5689cf3bc690e9ad20618ee3cf83e53c9d45899844
View on Chainz β†—

Height

#285,053

Difficulty

9.983672

Transactions

1

Size

208 B

Version

2

Bits

09fbd1e9

Nonce

50,332,512

Timestamp

11/30/2013, 8:49:25 AM

Confirmations

6,557,430

Merkle Root

b67b4a820c3f76b659fb4e57ea875a3dc917cfc1f595cca8ba8fe6ff9b51af05
Transactions (1)
Coinbaseb67b4a820c3f76…8fe6ff9b51af05
1 in β†’ 1 out10.0200 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.476 Γ— 10⁹⁹(100-digit number)
44768191209155575359…14605874901101936640
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
4.476 Γ— 10⁹⁹(100-digit number)
44768191209155575359…14605874901101936639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.953 Γ— 10⁹⁹(100-digit number)
89536382418311150719…29211749802203873279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.790 Γ— 10¹⁰⁰(101-digit number)
17907276483662230143…58423499604407746559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.581 Γ— 10¹⁰⁰(101-digit number)
35814552967324460287…16846999208815493119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.162 Γ— 10¹⁰⁰(101-digit number)
71629105934648920575…33693998417630986239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.432 Γ— 10¹⁰¹(102-digit number)
14325821186929784115…67387996835261972479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.865 Γ— 10¹⁰¹(102-digit number)
28651642373859568230…34775993670523944959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.730 Γ— 10¹⁰¹(102-digit number)
57303284747719136460…69551987341047889919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.146 Γ— 10¹⁰²(103-digit number)
11460656949543827292…39103974682095779839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.292 Γ— 10¹⁰²(103-digit number)
22921313899087654584…78207949364191559679
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 285053

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 75714c5ff9a0bf485e674d5689cf3bc690e9ad20618ee3cf83e53c9d45899844

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 #285,053 on Chainz β†—
Circulating Supply:57,984,282 XPMΒ·at block #6,842,482 Β· updates every 60s
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