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Home/Chain Registry/Block #2,856,820

Block #2,856,820

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/27/2018, 7:10:13 AM Β· Difficulty 11.6904 Β· 3,974,067 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
33f561d02748ec30a3e2d16701fb2cb95f8f91c5e63cd70d1f590f50cb439a56
View on Chainz β†—

Difficulty

11.690428

Transactions

1

Size

198 B

Version

2

Bits

0bb0bfe3

Nonce

1,405,025,617

Timestamp

9/27/2018, 7:10:13 AM

Confirmations

3,974,067

Merkle Root

92149cee81f5ea010a54eda55668bcc5fd9a1b29fd0a58b149715c5eadfb4863
Transactions (1)
Coinbase92149cee81f5ea…715c5eadfb4863
1 in β†’ 1 out7.3000 XPM109 B
AeR8oovx…iecEYRxc
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.

3.958 Γ— 10⁹²(93-digit number)
39585686998367049722…44910669512336561460
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
3.958 Γ— 10⁹²(93-digit number)
39585686998367049722…44910669512336561459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.917 Γ— 10⁹²(93-digit number)
79171373996734099445…89821339024673122919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.583 Γ— 10⁹³(94-digit number)
15834274799346819889…79642678049346245839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.166 Γ— 10⁹³(94-digit number)
31668549598693639778…59285356098692491679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.333 Γ— 10⁹³(94-digit number)
63337099197387279556…18570712197384983359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.266 Γ— 10⁹⁴(95-digit number)
12667419839477455911…37141424394769966719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.533 Γ— 10⁹⁴(95-digit number)
25334839678954911822…74282848789539933439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.066 Γ— 10⁹⁴(95-digit number)
50669679357909823644…48565697579079866879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.013 Γ— 10⁹⁡(96-digit number)
10133935871581964728…97131395158159733759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.026 Γ— 10⁹⁡(96-digit number)
20267871743163929457…94262790316319467519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.053 Γ— 10⁹⁡(96-digit number)
40535743486327858915…88525580632638935039
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 2856820

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 33f561d02748ec30a3e2d16701fb2cb95f8f91c5e63cd70d1f590f50cb439a56

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 #2,856,820 on Chainz β†—
Circulating Supply:57,891,233 XPMΒ·at block #6,830,886 Β· updates every 60s
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