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Home/Chain Registry/Block #2,796,300

Block #2,796,300

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/16/2018, 8:19:54 AM Β· Difficulty 11.6812 Β· 4,043,337 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6bd9ad4f2de8d3259801e2d8e4bdccb69f2a9f2c12706394be841b9a50c0f073
View on Chainz β†—

Difficulty

11.681208

Transactions

1

Size

200 B

Version

2

Bits

0bae63a1

Nonce

890,271,317

Timestamp

8/16/2018, 8:19:54 AM

Confirmations

4,043,337

Merkle Root

e46b48bbab9a8a23fc5fd3b976f581e7cf4bcb09b5e44659e04e910015c9b5a8
Transactions (1)
Coinbasee46b48bbab9a8a…4e910015c9b5a8
1 in β†’ 1 out7.3200 XPM110 B
AR3yzPjE…SQZPQm49
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.

5.248 Γ— 10⁹⁡(96-digit number)
52489291059892342682…72043770664626513920
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
5.248 Γ— 10⁹⁡(96-digit number)
52489291059892342682…72043770664626513921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.049 Γ— 10⁹⁢(97-digit number)
10497858211978468536…44087541329253027841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.099 Γ— 10⁹⁢(97-digit number)
20995716423956937072…88175082658506055681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.199 Γ— 10⁹⁢(97-digit number)
41991432847913874145…76350165317012111361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.398 Γ— 10⁹⁢(97-digit number)
83982865695827748291…52700330634024222721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.679 Γ— 10⁹⁷(98-digit number)
16796573139165549658…05400661268048445441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.359 Γ— 10⁹⁷(98-digit number)
33593146278331099316…10801322536096890881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.718 Γ— 10⁹⁷(98-digit number)
67186292556662198633…21602645072193781761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.343 Γ— 10⁹⁸(99-digit number)
13437258511332439726…43205290144387563521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.687 Γ— 10⁹⁸(99-digit number)
26874517022664879453…86410580288775127041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.374 Γ— 10⁹⁸(99-digit number)
53749034045329758906…72821160577550254081
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 2796300

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 6bd9ad4f2de8d3259801e2d8e4bdccb69f2a9f2c12706394be841b9a50c0f073

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 #2,796,300 on Chainz β†—
Circulating Supply:57,961,390 XPMΒ·at block #6,839,636 Β· updates every 60s
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