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Home/Chain Registry/Block #2,670,641

Block #2,670,641

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/20/2018, 11:57:00 PM Β· Difficulty 11.6850 Β· 4,170,791 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6f945c1dd190c2173cbd440b422e66f6188bce600b0f72ac3a78eb74b973a912
View on Chainz β†—

Difficulty

11.685001

Transactions

1

Size

199 B

Version

2

Bits

0baf5c35

Nonce

1,702,558,010

Timestamp

5/20/2018, 11:57:00 PM

Confirmations

4,170,791

Merkle Root

49d1902c4c9611109c069ad38a2c067a2eb9f6dceb2f4ba8dbbccf2824902e71
Transactions (1)
Coinbase49d1902c4c9611…bccf2824902e71
1 in β†’ 1 out7.3100 XPM110 B
AeLv5HJY…DK3JUq4y
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.

3.105 Γ— 10⁹²(93-digit number)
31052362720192254436…72740267447721904640
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
3.105 Γ— 10⁹²(93-digit number)
31052362720192254436…72740267447721904641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.210 Γ— 10⁹²(93-digit number)
62104725440384508873…45480534895443809281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.242 Γ— 10⁹³(94-digit number)
12420945088076901774…90961069790887618561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.484 Γ— 10⁹³(94-digit number)
24841890176153803549…81922139581775237121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.968 Γ— 10⁹³(94-digit number)
49683780352307607099…63844279163550474241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.936 Γ— 10⁹³(94-digit number)
99367560704615214198…27688558327100948481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.987 Γ— 10⁹⁴(95-digit number)
19873512140923042839…55377116654201896961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.974 Γ— 10⁹⁴(95-digit number)
39747024281846085679…10754233308403793921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.949 Γ— 10⁹⁴(95-digit number)
79494048563692171358…21508466616807587841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.589 Γ— 10⁹⁡(96-digit number)
15898809712738434271…43016933233615175681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.179 Γ— 10⁹⁡(96-digit number)
31797619425476868543…86033866467230351361
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 2670641

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 6f945c1dd190c2173cbd440b422e66f6188bce600b0f72ac3a78eb74b973a912

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 #2,670,641 on Chainz β†—
Circulating Supply:57,975,834 XPMΒ·at block #6,841,431 Β· updates every 60s
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