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Home/Chain Registry/Block #2,846,061

Block #2,846,061

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/19/2018, 8:11:13 AM Β· Difficulty 11.7301 Β· 3,994,853 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1ef86bcc54275942e74aa02eac4bfdb03bf97dd60de5907f30d33c0091143e97
View on Chainz β†—

Difficulty

11.730056

Transactions

1

Size

201 B

Version

2

Bits

0bbae4f7

Nonce

1,722,509,648

Timestamp

9/19/2018, 8:11:13 AM

Confirmations

3,994,853

Merkle Root

92922866c6f47794864b612e70b57e27151264dd1a4afc395c71924acf5aeafe
Transactions (1)
Coinbase92922866c6f477…71924acf5aeafe
1 in β†’ 1 out7.2600 XPM110 B
AHTfbzBS…ihMiuru2
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.

7.068 Γ— 10⁹⁢(97-digit number)
70684716384212305124…25649578203305653760
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
7.068 Γ— 10⁹⁢(97-digit number)
70684716384212305124…25649578203305653759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.413 Γ— 10⁹⁷(98-digit number)
14136943276842461024…51299156406611307519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.827 Γ— 10⁹⁷(98-digit number)
28273886553684922049…02598312813222615039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.654 Γ— 10⁹⁷(98-digit number)
56547773107369844099…05196625626445230079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.130 Γ— 10⁹⁸(99-digit number)
11309554621473968819…10393251252890460159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.261 Γ— 10⁹⁸(99-digit number)
22619109242947937639…20786502505780920319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.523 Γ— 10⁹⁸(99-digit number)
45238218485895875279…41573005011561840639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.047 Γ— 10⁹⁸(99-digit number)
90476436971791750558…83146010023123681279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.809 Γ— 10⁹⁹(100-digit number)
18095287394358350111…66292020046247362559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.619 Γ— 10⁹⁹(100-digit number)
36190574788716700223…32584040092494725119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.238 Γ— 10⁹⁹(100-digit number)
72381149577433400447…65168080184989450239
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 2846061

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 1ef86bcc54275942e74aa02eac4bfdb03bf97dd60de5907f30d33c0091143e97

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 #2,846,061 on Chainz β†—
Circulating Supply:57,971,662 XPMΒ·at block #6,840,913 Β· updates every 60s
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