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Home/Chain Registry/Block #2,870,658

Block #2,870,658

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/7/2018, 4:19:55 AM Β· Difficulty 11.6658 Β· 3,972,831 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dabfc09bb936f30c43fe45e73b91d989a28fe30c44745272c5991641963dc8ac
View on Chainz β†—

Difficulty

11.665778

Transactions

1

Size

201 B

Version

2

Bits

0baa7071

Nonce

20,721,892

Timestamp

10/7/2018, 4:19:55 AM

Confirmations

3,972,831

Merkle Root

146022a0b6f9dd0477e6cacaf72d10158a95cf497e8b633a5cbd1d5e189b651d
Transactions (1)
Coinbase146022a0b6f9dd…bd1d5e189b651d
1 in β†’ 1 out7.3400 XPM110 B
AdBKhXvS…dtryPfWU
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.

5.509 Γ— 10⁹⁢(97-digit number)
55091368634103337807…88502949451575861760
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
5.509 Γ— 10⁹⁢(97-digit number)
55091368634103337807…88502949451575861759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.101 Γ— 10⁹⁷(98-digit number)
11018273726820667561…77005898903151723519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.203 Γ— 10⁹⁷(98-digit number)
22036547453641335122…54011797806303447039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.407 Γ— 10⁹⁷(98-digit number)
44073094907282670245…08023595612606894079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.814 Γ— 10⁹⁷(98-digit number)
88146189814565340491…16047191225213788159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.762 Γ— 10⁹⁸(99-digit number)
17629237962913068098…32094382450427576319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.525 Γ— 10⁹⁸(99-digit number)
35258475925826136196…64188764900855152639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.051 Γ— 10⁹⁸(99-digit number)
70516951851652272393…28377529801710305279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.410 Γ— 10⁹⁹(100-digit number)
14103390370330454478…56755059603420610559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.820 Γ— 10⁹⁹(100-digit number)
28206780740660908957…13510119206841221119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.641 Γ— 10⁹⁹(100-digit number)
56413561481321817914…27020238413682442239
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 2870658

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 dabfc09bb936f30c43fe45e73b91d989a28fe30c44745272c5991641963dc8ac

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 #2,870,658 on Chainz β†—
Circulating Supply:57,992,283 XPMΒ·at block #6,843,488 Β· updates every 60s
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