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Home/Chain Registry/Block #2,943,278

Block #2,943,278

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2018, 5:09:41 PM Β· Difficulty 11.3938 Β· 3,897,802 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9f8ce2fd9bafd457f2aafe344cd71994bfbc08821f4589723e70a94c8d455c18
View on Chainz β†—

Difficulty

11.393844

Transactions

1

Size

201 B

Version

2

Bits

0b64d2ef

Nonce

1,077,527,785

Timestamp

11/28/2018, 5:09:41 PM

Confirmations

3,897,802

Merkle Root

4163c4021afeb22db30f5727c16957824a5ed264042813e0cceb2de288c74132
Transactions (1)
Coinbase4163c4021afeb2…eb2de288c74132
1 in β†’ 1 out7.6900 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.045 Γ— 10⁹⁢(97-digit number)
20452863576247841060…46116944073018547200
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
2.045 Γ— 10⁹⁢(97-digit number)
20452863576247841060…46116944073018547201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.090 Γ— 10⁹⁢(97-digit number)
40905727152495682121…92233888146037094401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.181 Γ— 10⁹⁢(97-digit number)
81811454304991364242…84467776292074188801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.636 Γ— 10⁹⁷(98-digit number)
16362290860998272848…68935552584148377601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.272 Γ— 10⁹⁷(98-digit number)
32724581721996545696…37871105168296755201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.544 Γ— 10⁹⁷(98-digit number)
65449163443993091393…75742210336593510401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.308 Γ— 10⁹⁸(99-digit number)
13089832688798618278…51484420673187020801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.617 Γ— 10⁹⁸(99-digit number)
26179665377597236557…02968841346374041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.235 Γ— 10⁹⁸(99-digit number)
52359330755194473114…05937682692748083201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.047 Γ— 10⁹⁹(100-digit number)
10471866151038894622…11875365385496166401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.094 Γ— 10⁹⁹(100-digit number)
20943732302077789245…23750730770992332801
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 2943278

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 9f8ce2fd9bafd457f2aafe344cd71994bfbc08821f4589723e70a94c8d455c18

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 #2,943,278 on Chainz β†—
Circulating Supply:57,973,002 XPMΒ·at block #6,841,079 Β· updates every 60s
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