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Home/Chain Registry/Block #2,802,278

Block #2,802,278

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2018, 2:42:45 PM Β· Difficulty 11.6709 Β· 4,039,304 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c27f9296c8cb659605cd89cf5938841a43d21d5ed9c14b22fa56b28cf618a5d1
View on Chainz β†—

Difficulty

11.670895

Transactions

1

Size

201 B

Version

2

Bits

0babbfc1

Nonce

1,922,960,551

Timestamp

8/20/2018, 2:42:45 PM

Confirmations

4,039,304

Merkle Root

a15a8aefe1adc8ae548fffedc826c7abfb16dcc28c3a10a767d64a4c801f87ec
Transactions (1)
Coinbasea15a8aefe1adc8…d64a4c801f87ec
1 in β†’ 1 out7.3300 XPM110 B
AY3NLnWS…FGFwdhC9
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.

2.415 Γ— 10⁹⁢(97-digit number)
24152678685964234663…59351656381411952640
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
2.415 Γ— 10⁹⁢(97-digit number)
24152678685964234663…59351656381411952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.830 Γ— 10⁹⁢(97-digit number)
48305357371928469326…18703312762823905281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.661 Γ— 10⁹⁢(97-digit number)
96610714743856938652…37406625525647810561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.932 Γ— 10⁹⁷(98-digit number)
19322142948771387730…74813251051295621121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.864 Γ— 10⁹⁷(98-digit number)
38644285897542775461…49626502102591242241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.728 Γ— 10⁹⁷(98-digit number)
77288571795085550922…99253004205182484481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.545 Γ— 10⁹⁸(99-digit number)
15457714359017110184…98506008410364968961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.091 Γ— 10⁹⁸(99-digit number)
30915428718034220368…97012016820729937921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.183 Γ— 10⁹⁸(99-digit number)
61830857436068440737…94024033641459875841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.236 Γ— 10⁹⁹(100-digit number)
12366171487213688147…88048067282919751681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.473 Γ— 10⁹⁹(100-digit number)
24732342974427376295…76096134565839503361
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 2802278

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 c27f9296c8cb659605cd89cf5938841a43d21d5ed9c14b22fa56b28cf618a5d1

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 #2,802,278 on Chainz β†—
Circulating Supply:57,977,042 XPMΒ·at block #6,841,581 Β· updates every 60s
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