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Home/Chain Registry/Block #2,045,986

Block #2,045,986

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/31/2017, 2:14:23 AM Β· Difficulty 10.6838 Β· 4,794,461 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c79066c9a307210f5c0053ba6c19df039d11d1777df7ffd9a8e945d130a9a267
View on Chainz β†—

Difficulty

10.683780

Transactions

1

Size

200 B

Version

2

Bits

0aaf0c36

Nonce

425,971,657

Timestamp

3/31/2017, 2:14:23 AM

Confirmations

4,794,461

Merkle Root

e1ab0f63b5a526fcbac319cb9b7fa2ebb34eb8f15cd6a7080892acafc30b81d4
Transactions (1)
Coinbasee1ab0f63b5a526…92acafc30b81d4
1 in β†’ 1 out8.7500 XPM109 B
AUVZmGD5…jh6xgNHy
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.

1.655 Γ— 10⁹⁷(98-digit number)
16552583106810338747…88957545614770124800
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
1.655 Γ— 10⁹⁷(98-digit number)
16552583106810338747…88957545614770124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.310 Γ— 10⁹⁷(98-digit number)
33105166213620677494…77915091229540249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.621 Γ— 10⁹⁷(98-digit number)
66210332427241354989…55830182459080499199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.324 Γ— 10⁹⁸(99-digit number)
13242066485448270997…11660364918160998399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.648 Γ— 10⁹⁸(99-digit number)
26484132970896541995…23320729836321996799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.296 Γ— 10⁹⁸(99-digit number)
52968265941793083991…46641459672643993599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.059 Γ— 10⁹⁹(100-digit number)
10593653188358616798…93282919345287987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.118 Γ— 10⁹⁹(100-digit number)
21187306376717233596…86565838690575974399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.237 Γ— 10⁹⁹(100-digit number)
42374612753434467193…73131677381151948799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.474 Γ— 10⁹⁹(100-digit number)
84749225506868934386…46263354762303897599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2045986

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 c79066c9a307210f5c0053ba6c19df039d11d1777df7ffd9a8e945d130a9a267

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 #2,045,986 on Chainz β†—
Circulating Supply:57,967,906 XPMΒ·at block #6,840,446 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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