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Home/Chain Registry/Block #2,639,072

Block #2,639,072

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 12:43:40 PM Β· Difficulty 11.5209 Β· 4,204,788 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
83e70c5322ba100de06709a1ec2ac798aaeeb12fe3e1fb0a899a91e46e604ec0
View on Chainz β†—

Difficulty

11.520867

Transactions

1

Size

200 B

Version

2

Bits

0b855791

Nonce

290,137,993

Timestamp

4/30/2018, 12:43:40 PM

Confirmations

4,204,788

Merkle Root

7ce4f46838b5add7be3e9dd7fa2812e4dbea698acd44a9a81ad02c2ec8db4f46
Transactions (1)
Coinbase7ce4f46838b5ad…d02c2ec8db4f46
1 in β†’ 1 out7.5200 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.634 Γ— 10⁹⁡(96-digit number)
16343215265247543437…86764361592553064800
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
1.634 Γ— 10⁹⁡(96-digit number)
16343215265247543437…86764361592553064801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.268 Γ— 10⁹⁡(96-digit number)
32686430530495086875…73528723185106129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.537 Γ— 10⁹⁡(96-digit number)
65372861060990173750…47057446370212259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.307 Γ— 10⁹⁢(97-digit number)
13074572212198034750…94114892740424518401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.614 Γ— 10⁹⁢(97-digit number)
26149144424396069500…88229785480849036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.229 Γ— 10⁹⁢(97-digit number)
52298288848792139000…76459570961698073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.045 Γ— 10⁹⁷(98-digit number)
10459657769758427800…52919141923396147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.091 Γ— 10⁹⁷(98-digit number)
20919315539516855600…05838283846792294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.183 Γ— 10⁹⁷(98-digit number)
41838631079033711200…11676567693584588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.367 Γ— 10⁹⁷(98-digit number)
83677262158067422400…23353135387169177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.673 Γ— 10⁹⁸(99-digit number)
16735452431613484480…46706270774338355201
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 2639072

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 83e70c5322ba100de06709a1ec2ac798aaeeb12fe3e1fb0a899a91e46e604ec0

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 #2,639,072 on Chainz β†—
Circulating Supply:57,995,248 XPMΒ·at block #6,843,859 Β· updates every 60s
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