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Home/Chain Registry/Block #3,002,765

Block #3,002,765

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/10/2019, 12:04:02 AM Β· Difficulty 11.2015 Β· 3,824,203 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2e9000097cabda4d433bcb2807b2f78c969df35bc4672a45c16da29d30bf998
View on Chainz β†—

Difficulty

11.201503

Transactions

1

Size

200 B

Version

2

Bits

0b3395ac

Nonce

727,459,076

Timestamp

1/10/2019, 12:04:02 AM

Confirmations

3,824,203

Merkle Root

b61bbfe6a66471b1405c5df95fe011421a542585126f78127fb08ffcb9f8a9b1
Transactions (1)
Coinbaseb61bbfe6a66471…b08ffcb9f8a9b1
1 in β†’ 1 out7.9600 XPM109 B
AbXwmGxD…4XXYP765
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.

1.303 Γ— 10⁹⁢(97-digit number)
13030848481351359677…65026002598184222720
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
1.303 Γ— 10⁹⁢(97-digit number)
13030848481351359677…65026002598184222721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.606 Γ— 10⁹⁢(97-digit number)
26061696962702719354…30052005196368445441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.212 Γ— 10⁹⁢(97-digit number)
52123393925405438708…60104010392736890881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.042 Γ— 10⁹⁷(98-digit number)
10424678785081087741…20208020785473781761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.084 Γ— 10⁹⁷(98-digit number)
20849357570162175483…40416041570947563521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.169 Γ— 10⁹⁷(98-digit number)
41698715140324350966…80832083141895127041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.339 Γ— 10⁹⁷(98-digit number)
83397430280648701933…61664166283790254081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.667 Γ— 10⁹⁸(99-digit number)
16679486056129740386…23328332567580508161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.335 Γ— 10⁹⁸(99-digit number)
33358972112259480773…46656665135161016321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.671 Γ— 10⁹⁸(99-digit number)
66717944224518961546…93313330270322032641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.334 Γ— 10⁹⁹(100-digit number)
13343588844903792309…86626660540644065281
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 3002765

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 d2e9000097cabda4d433bcb2807b2f78c969df35bc4672a45c16da29d30bf998

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 #3,002,765 on Chainz β†—
Circulating Supply:57,859,920 XPMΒ·at block #6,826,967 Β· updates every 60s
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