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Home/Chain Registry/Block #2,719,791

Block #2,719,791

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/24/2018, 8:51:43 PM Β· Difficulty 11.6128 Β· 4,123,101 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d251636ada721ee62601fcf38d7c443156cac28f2c415af360cbe84cbc2ff750
View on Chainz β†—

Difficulty

11.612848

Transactions

1

Size

200 B

Version

2

Bits

0b9ce396

Nonce

841,284,067

Timestamp

6/24/2018, 8:51:43 PM

Confirmations

4,123,101

Merkle Root

931cb727c9b5aa58bafe363d540db7e03138bbe606e22bd132ee0b0e4f88d685
Transactions (1)
Coinbase931cb727c9b5aa…ee0b0e4f88d685
1 in β†’ 1 out7.4000 XPM110 B
AH8taCeD…Sk3zD1rm
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.

1.056 Γ— 10⁹⁴(95-digit number)
10563336054071735680…05553387289542897550
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
1.056 Γ— 10⁹⁴(95-digit number)
10563336054071735680…05553387289542897551
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.112 Γ— 10⁹⁴(95-digit number)
21126672108143471361…11106774579085795101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.225 Γ— 10⁹⁴(95-digit number)
42253344216286942722…22213549158171590201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.450 Γ— 10⁹⁴(95-digit number)
84506688432573885445…44427098316343180401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.690 Γ— 10⁹⁡(96-digit number)
16901337686514777089…88854196632686360801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.380 Γ— 10⁹⁡(96-digit number)
33802675373029554178…77708393265372721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.760 Γ— 10⁹⁡(96-digit number)
67605350746059108356…55416786530745443201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.352 Γ— 10⁹⁢(97-digit number)
13521070149211821671…10833573061490886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.704 Γ— 10⁹⁢(97-digit number)
27042140298423643342…21667146122981772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.408 Γ— 10⁹⁢(97-digit number)
54084280596847286684…43334292245963545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.081 Γ— 10⁹⁷(98-digit number)
10816856119369457336…86668584491927091201
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 2719791

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 d251636ada721ee62601fcf38d7c443156cac28f2c415af360cbe84cbc2ff750

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 #2,719,791 on Chainz β†—
Circulating Supply:57,987,483 XPMΒ·at block #6,842,891 Β· updates every 60s
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