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Home/Chain Registry/Block #2,649,311

Block #2,649,311

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2018, 3:45:53 AM Β· Difficulty 11.7646 Β· 4,181,447 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
19e82d2aaaa1b2bc3d28fe15272d8f57e6801f6d01c5a2fc1a797462386ca371
View on Chainz β†—

Difficulty

11.764641

Transactions

1

Size

200 B

Version

2

Bits

0bc3bf81

Nonce

155,962,801

Timestamp

5/5/2018, 3:45:53 AM

Confirmations

4,181,447

Merkle Root

863e50d7e290a41e046003638f31e073a6ab4269b0405d8897c3f4b8cb11b7a8
Transactions (1)
Coinbase863e50d7e290a4…c3f4b8cb11b7a8
1 in β†’ 1 out7.2100 XPM110 B
Adqah8zh…1WwoHJ9t
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.

3.193 Γ— 10⁹⁴(95-digit number)
31933977378283104344…73181177027461477120
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
3.193 Γ— 10⁹⁴(95-digit number)
31933977378283104344…73181177027461477121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.386 Γ— 10⁹⁴(95-digit number)
63867954756566208689…46362354054922954241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.277 Γ— 10⁹⁡(96-digit number)
12773590951313241737…92724708109845908481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.554 Γ— 10⁹⁡(96-digit number)
25547181902626483475…85449416219691816961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.109 Γ— 10⁹⁡(96-digit number)
51094363805252966951…70898832439383633921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.021 Γ— 10⁹⁢(97-digit number)
10218872761050593390…41797664878767267841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.043 Γ— 10⁹⁢(97-digit number)
20437745522101186780…83595329757534535681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.087 Γ— 10⁹⁢(97-digit number)
40875491044202373561…67190659515069071361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.175 Γ— 10⁹⁢(97-digit number)
81750982088404747122…34381319030138142721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.635 Γ— 10⁹⁷(98-digit number)
16350196417680949424…68762638060276285441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.270 Γ— 10⁹⁷(98-digit number)
32700392835361898848…37525276120552570881
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 2649311

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 19e82d2aaaa1b2bc3d28fe15272d8f57e6801f6d01c5a2fc1a797462386ca371

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 #2,649,311 on Chainz β†—
Circulating Supply:57,890,201 XPMΒ·at block #6,830,757 Β· updates every 60s
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