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Home/Chain Registry/Block #2,990,135

Block #2,990,135

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/31/2018, 11:29:53 PM Β· Difficulty 11.2567 Β· 3,855,520 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
79af18270fd07c7000529e73b37e70736bc162457ce210c359ce49ba07546ff1
View on Chainz β†—

Difficulty

11.256651

Transactions

1

Size

200 B

Version

2

Bits

0b41b3e8

Nonce

1,125,308,757

Timestamp

12/31/2018, 11:29:53 PM

Confirmations

3,855,520

Merkle Root

c87b1d1f00f1a51c78e072c49e1ff6201683fd90bef0797b577c32b861f62e57
Transactions (1)
Coinbasec87b1d1f00f1a5…7c32b861f62e57
1 in β†’ 1 out7.8800 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.

6.286 Γ— 10⁹³(94-digit number)
62864048090383589310…42791141068842526320
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.286 Γ— 10⁹³(94-digit number)
62864048090383589310…42791141068842526321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.257 Γ— 10⁹⁴(95-digit number)
12572809618076717862…85582282137685052641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.514 Γ— 10⁹⁴(95-digit number)
25145619236153435724…71164564275370105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.029 Γ— 10⁹⁴(95-digit number)
50291238472306871448…42329128550740210561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.005 Γ— 10⁹⁡(96-digit number)
10058247694461374289…84658257101480421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.011 Γ— 10⁹⁡(96-digit number)
20116495388922748579…69316514202960842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.023 Γ— 10⁹⁡(96-digit number)
40232990777845497158…38633028405921684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.046 Γ— 10⁹⁡(96-digit number)
80465981555690994317…77266056811843368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.609 Γ— 10⁹⁢(97-digit number)
16093196311138198863…54532113623686737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.218 Γ— 10⁹⁢(97-digit number)
32186392622276397727…09064227247373475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.437 Γ— 10⁹⁢(97-digit number)
64372785244552795454…18128454494746951681
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2990135

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 79af18270fd07c7000529e73b37e70736bc162457ce210c359ce49ba07546ff1

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 #2,990,135 on Chainz β†—
Circulating Supply:58,009,689 XPMΒ·at block #6,845,654 Β· updates every 60s
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