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Home/Chain Registry/Block #2,081,131

Block #2,081,131

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/21/2017, 1:04:38 PM Β· Difficulty 10.8652 Β· 4,757,206 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
78860ec6407ef9a2afd4269d568200cd06c5f004856090e581f32dfbb8e4e40a
View on Chainz β†—

Difficulty

10.865195

Transactions

1

Size

208 B

Version

2

Bits

0add7d66

Nonce

56,478,213

Timestamp

4/21/2017, 1:04:38 PM

Confirmations

4,757,206

Merkle Root

adc10a5e718b417fd8de3aa5908a545e46dbd883ee745eb73b978fca5ddcf580
Transactions (1)
Coinbaseadc10a5e718b41…978fca5ddcf580
1 in β†’ 1 out8.4600 XPM118 B
AM6GYpjw…aw86QDtR
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.

3.306 Γ— 10⁹⁡(96-digit number)
33065810809462305020…31876608361807087000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.306 Γ— 10⁹⁡(96-digit number)
33065810809462305020…31876608361807086999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.613 Γ— 10⁹⁡(96-digit number)
66131621618924610040…63753216723614173999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.322 Γ— 10⁹⁢(97-digit number)
13226324323784922008…27506433447228347999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.645 Γ— 10⁹⁢(97-digit number)
26452648647569844016…55012866894456695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.290 Γ— 10⁹⁢(97-digit number)
52905297295139688032…10025733788913391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.058 Γ— 10⁹⁷(98-digit number)
10581059459027937606…20051467577826783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.116 Γ— 10⁹⁷(98-digit number)
21162118918055875213…40102935155653567999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.232 Γ— 10⁹⁷(98-digit number)
42324237836111750426…80205870311307135999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.464 Γ— 10⁹⁷(98-digit number)
84648475672223500852…60411740622614271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.692 Γ— 10⁹⁸(99-digit number)
16929695134444700170…20823481245228543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.385 Γ— 10⁹⁸(99-digit number)
33859390268889400340…41646962490457087999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2081131

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 78860ec6407ef9a2afd4269d568200cd06c5f004856090e581f32dfbb8e4e40a

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 #2,081,131 on Chainz β†—
Circulating Supply:57,950,973 XPMΒ·at block #6,838,336 Β· updates every 60s
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