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Home/Chain Registry/Block #3,081,069

Block #3,081,069

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/6/2019, 1:14:48 PM Β· Difficulty 11.0222 Β· 3,762,114 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3f56d542e5cdb1415c0fe1727e6a87ae08e0e933a25958ab08dfca582eb30a02
View on Chainz β†—

Difficulty

11.022156

Transactions

1

Size

200 B

Version

2

Bits

0b05ac03

Nonce

1,485,124,011

Timestamp

3/6/2019, 1:14:48 PM

Confirmations

3,762,114

Merkle Root

5913ca79894943b8a2fb3f14fa2aa9432e6138da1a5a08bde9eb3fe71823aa77
Transactions (1)
Coinbase5913ca79894943…eb3fe71823aa77
1 in β†’ 1 out8.2200 XPM110 B
AbXwmGxD…4XXYP765
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.

9.620 Γ— 10⁹⁴(95-digit number)
96206978447480986590…86082937711315639520
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
9.620 Γ— 10⁹⁴(95-digit number)
96206978447480986590…86082937711315639519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.924 Γ— 10⁹⁡(96-digit number)
19241395689496197318…72165875422631279039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.848 Γ— 10⁹⁡(96-digit number)
38482791378992394636…44331750845262558079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.696 Γ— 10⁹⁡(96-digit number)
76965582757984789272…88663501690525116159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.539 Γ— 10⁹⁢(97-digit number)
15393116551596957854…77327003381050232319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.078 Γ— 10⁹⁢(97-digit number)
30786233103193915709…54654006762100464639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.157 Γ— 10⁹⁢(97-digit number)
61572466206387831418…09308013524200929279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.231 Γ— 10⁹⁷(98-digit number)
12314493241277566283…18616027048401858559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.462 Γ— 10⁹⁷(98-digit number)
24628986482555132567…37232054096803717119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.925 Γ— 10⁹⁷(98-digit number)
49257972965110265134…74464108193607434239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.851 Γ— 10⁹⁷(98-digit number)
98515945930220530269…48928216387214868479
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 3081069

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 3f56d542e5cdb1415c0fe1727e6a87ae08e0e933a25958ab08dfca582eb30a02

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 #3,081,069 on Chainz β†—
Circulating Supply:57,989,832 XPMΒ·at block #6,843,182 Β· updates every 60s
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