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Home/Chain Registry/Block #2,850,878

Block #2,850,878

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/22/2018, 4:34:14 PM Β· Difficulty 11.7299 Β· 3,976,049 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d0ca99fea4efd1615dee5567dc3fdb89fbfcf62d5fe837ff0b94227327761e86
View on Chainz β†—

Difficulty

11.729937

Transactions

2

Size

37.00 KB

Version

2

Bits

0bbadd23

Nonce

793,296,549

Timestamp

9/22/2018, 4:34:14 PM

Confirmations

3,976,049

Merkle Root

44dbbc739894a650a643b898036ae0b6830697c0906d4ddf93627fbce4312c1b
Transactions (2)
Coinbaseaabf5c6b3fc076…02a33725540478
1 in β†’ 1 out7.6400 XPM110 B
AUMQRepm…tAfKmdW1
e23f2f0de84c1b…2e1588b2cad795
254 in β†’ 2 out26500.6362 XPM36.80 KB
AYqUZT5S…Le8qLwx9ALuqyTnd…h2XkaoFU
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.

3.390 Γ— 10⁹⁴(95-digit number)
33904156071967087497…76063457478685056000
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
3.390 Γ— 10⁹⁴(95-digit number)
33904156071967087497…76063457478685056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.780 Γ— 10⁹⁴(95-digit number)
67808312143934174994…52126914957370112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.356 Γ— 10⁹⁡(96-digit number)
13561662428786834998…04253829914740224001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.712 Γ— 10⁹⁡(96-digit number)
27123324857573669997…08507659829480448001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.424 Γ— 10⁹⁡(96-digit number)
54246649715147339995…17015319658960896001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.084 Γ— 10⁹⁢(97-digit number)
10849329943029467999…34030639317921792001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.169 Γ— 10⁹⁢(97-digit number)
21698659886058935998…68061278635843584001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.339 Γ— 10⁹⁢(97-digit number)
43397319772117871996…36122557271687168001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.679 Γ— 10⁹⁢(97-digit number)
86794639544235743993…72245114543374336001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.735 Γ— 10⁹⁷(98-digit number)
17358927908847148798…44490229086748672001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.471 Γ— 10⁹⁷(98-digit number)
34717855817694297597…88980458173497344001
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 2850878

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 d0ca99fea4efd1615dee5567dc3fdb89fbfcf62d5fe837ff0b94227327761e86

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 #2,850,878 on Chainz β†—
Circulating Supply:57,859,587 XPMΒ·at block #6,826,926 Β· updates every 60s
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