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Home/Chain Registry/Block #3,086,852

Block #3,086,852

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/10/2019, 12:19:00 PM Β· Difficulty 11.0375 Β· 3,756,708 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2bb03e3c23d3234c7b19119c5c37327104e0a27ae48d1e9cd133f95cb537c1f4
View on Chainz β†—

Difficulty

11.037456

Transactions

1

Size

199 B

Version

2

Bits

0b0996bc

Nonce

1,887,846,128

Timestamp

3/10/2019, 12:19:00 PM

Confirmations

3,756,708

Merkle Root

db0953ed92fcfb3f8c14febcbf36d59b8e1fd098f0a766d9c8af645187d84752
Transactions (1)
Coinbasedb0953ed92fcfb…af645187d84752
1 in β†’ 1 out8.2000 XPM109 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.

7.583 Γ— 10⁹⁴(95-digit number)
75834818859550499701…11319373817420660560
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
7.583 Γ— 10⁹⁴(95-digit number)
75834818859550499701…11319373817420660559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.516 Γ— 10⁹⁡(96-digit number)
15166963771910099940…22638747634841321119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.033 Γ— 10⁹⁡(96-digit number)
30333927543820199880…45277495269682642239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.066 Γ— 10⁹⁡(96-digit number)
60667855087640399761…90554990539365284479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.213 Γ— 10⁹⁢(97-digit number)
12133571017528079952…81109981078730568959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.426 Γ— 10⁹⁢(97-digit number)
24267142035056159904…62219962157461137919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.853 Γ— 10⁹⁢(97-digit number)
48534284070112319809…24439924314922275839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.706 Γ— 10⁹⁢(97-digit number)
97068568140224639618…48879848629844551679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.941 Γ— 10⁹⁷(98-digit number)
19413713628044927923…97759697259689103359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.882 Γ— 10⁹⁷(98-digit number)
38827427256089855847…95519394519378206719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.765 Γ— 10⁹⁷(98-digit number)
77654854512179711694…91038789038756413439
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 3086852

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 2bb03e3c23d3234c7b19119c5c37327104e0a27ae48d1e9cd133f95cb537c1f4

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 #3,086,852 on Chainz β†—
Circulating Supply:57,992,855 XPMΒ·at block #6,843,559 Β· updates every 60s
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