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Home/Chain Registry/Block #2,647,162

Block #2,647,162

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 6:59:38 PM Β· Difficulty 11.7559 Β· 4,191,481 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
188f49e21e30f503f6e25c8bf2a56978c95c6cce1a231a0c1d4df25873eee1eb
View on Chainz β†—

Difficulty

11.755896

Transactions

3

Size

730 B

Version

2

Bits

0bc18268

Nonce

1,498,341,876

Timestamp

5/3/2018, 6:59:38 PM

Confirmations

4,191,481

Merkle Root

386d5b1efa688734410ba87e7ccde8f9f0ea0414b2f29dbf8e92bfb07af29250
Transactions (3)
Coinbasea8065b2b9c3c25…30ccec5668b01a
1 in β†’ 1 out7.2400 XPM110 B
ATmrFgj9…GM88j96H
f2671c96594ec1…42b99f7a7fde3c
2 in β†’ 2 out10.5887 XPM339 B
AdXRVNpe…B7YQLG3aAHSpfNV1…3SN848gr
11284b1a223452…4ad70593101177
1 in β†’ 2 out7.2800 XPM191 B
AUEs5Xs4…vsho9gUHAV3JM4zu…4Yqk98pg
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.

9.696 Γ— 10⁹³(94-digit number)
96968990867604370013…32082837774550841000
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
9.696 Γ— 10⁹³(94-digit number)
96968990867604370013…32082837774550841001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.939 Γ— 10⁹⁴(95-digit number)
19393798173520874002…64165675549101682001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.878 Γ— 10⁹⁴(95-digit number)
38787596347041748005…28331351098203364001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.757 Γ— 10⁹⁴(95-digit number)
77575192694083496011…56662702196406728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.551 Γ— 10⁹⁡(96-digit number)
15515038538816699202…13325404392813456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.103 Γ— 10⁹⁡(96-digit number)
31030077077633398404…26650808785626912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.206 Γ— 10⁹⁡(96-digit number)
62060154155266796808…53301617571253824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.241 Γ— 10⁹⁢(97-digit number)
12412030831053359361…06603235142507648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.482 Γ— 10⁹⁢(97-digit number)
24824061662106718723…13206470285015296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.964 Γ— 10⁹⁢(97-digit number)
49648123324213437447…26412940570030592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.929 Γ— 10⁹⁢(97-digit number)
99296246648426874894…52825881140061184001
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 2647162

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 188f49e21e30f503f6e25c8bf2a56978c95c6cce1a231a0c1d4df25873eee1eb

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 #2,647,162 on Chainz β†—
Circulating Supply:57,953,409 XPMΒ·at block #6,838,642 Β· updates every 60s
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