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Home/Chain Registry/Block #2,255,827

Block #2,255,827

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/17/2017, 2:32:27 PM Β· Difficulty 10.9506 Β· 4,589,527 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a36ca930f9da7ff168641a240c2dae3ddf72a703a77f7ce7e7600c6f739f4601
View on Chainz β†—

Difficulty

10.950600

Transactions

1

Size

200 B

Version

2

Bits

0af35a81

Nonce

1,273,995,898

Timestamp

8/17/2017, 2:32:27 PM

Confirmations

4,589,527

Merkle Root

0d02774a845bfcd0bded5a3dd662ea7cf350a965f03d090ce522641270f3c807
Transactions (1)
Coinbase0d02774a845bfc…22641270f3c807
1 in β†’ 1 out8.3300 XPM109 B
AHGhBGmV…ZNQEi8kd
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.

5.920 Γ— 10⁹⁢(97-digit number)
59203650847819906678…74174296732799395840
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
5.920 Γ— 10⁹⁢(97-digit number)
59203650847819906678…74174296732799395839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.184 Γ— 10⁹⁷(98-digit number)
11840730169563981335…48348593465598791679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.368 Γ— 10⁹⁷(98-digit number)
23681460339127962671…96697186931197583359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.736 Γ— 10⁹⁷(98-digit number)
47362920678255925342…93394373862395166719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.472 Γ— 10⁹⁷(98-digit number)
94725841356511850685…86788747724790333439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.894 Γ— 10⁹⁸(99-digit number)
18945168271302370137…73577495449580666879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.789 Γ— 10⁹⁸(99-digit number)
37890336542604740274…47154990899161333759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.578 Γ— 10⁹⁸(99-digit number)
75780673085209480548…94309981798322667519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.515 Γ— 10⁹⁹(100-digit number)
15156134617041896109…88619963596645335039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.031 Γ— 10⁹⁹(100-digit number)
30312269234083792219…77239927193290670079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.062 Γ— 10⁹⁹(100-digit number)
60624538468167584438…54479854386581340159
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 2255827

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 a36ca930f9da7ff168641a240c2dae3ddf72a703a77f7ce7e7600c6f739f4601

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 #2,255,827 on Chainz β†—
Circulating Supply:58,007,275 XPMΒ·at block #6,845,353 Β· updates every 60s
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