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Block #2,802,476

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/20/2018, 6:12:44 PM Β· Difficulty 11.6701 Β· 4,042,817 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7d1833f03a4c695a7bc4e0f9a9868bab237b907793ec96b0cc75010355a58b16
View on Chainz β†—

Difficulty

11.670087

Transactions

1

Size

201 B

Version

2

Bits

0bab8acd

Nonce

31,717,395

Timestamp

8/20/2018, 6:12:44 PM

Confirmations

4,042,817

Merkle Root

8a5c97d71734cf5fec3cb6808443641bab5379c9a0e5b64afce4b8ce65445681
Transactions (1)
Coinbase8a5c97d71734cf…e4b8ce65445681
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.176 Γ— 10⁹⁢(97-digit number)
21764491781819007686…82610531076896153600
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
2.176 Γ— 10⁹⁢(97-digit number)
21764491781819007686…82610531076896153599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.352 Γ— 10⁹⁢(97-digit number)
43528983563638015373…65221062153792307199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.705 Γ— 10⁹⁢(97-digit number)
87057967127276030747…30442124307584614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.741 Γ— 10⁹⁷(98-digit number)
17411593425455206149…60884248615169228799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.482 Γ— 10⁹⁷(98-digit number)
34823186850910412298…21768497230338457599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.964 Γ— 10⁹⁷(98-digit number)
69646373701820824597…43536994460676915199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁸(99-digit number)
13929274740364164919…87073988921353830399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.785 Γ— 10⁹⁸(99-digit number)
27858549480728329839…74147977842707660799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.571 Γ— 10⁹⁸(99-digit number)
55717098961456659678…48295955685415321599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.114 Γ— 10⁹⁹(100-digit number)
11143419792291331935…96591911370830643199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.228 Γ— 10⁹⁹(100-digit number)
22286839584582663871…93183822741661286399
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 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
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 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 2802476

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 7d1833f03a4c695a7bc4e0f9a9868bab237b907793ec96b0cc75010355a58b16

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 #2,802,476 on Chainz β†—
Circulating Supply:58,006,782 XPMΒ·at block #6,845,292 Β· updates every 60s
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