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Home/Chain Registry/Block #2,867,681

Block #2,867,681

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/5/2018, 2:26:33 AM Β· Difficulty 11.6667 Β· 3,966,006 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
42dc1a733ccd3fb50833c818a004acb32cc8053e141dfa42eb9da3414ee94601
View on Chainz β†—

Difficulty

11.666693

Transactions

1

Size

200 B

Version

2

Bits

0baaac60

Nonce

1,859,370,095

Timestamp

10/5/2018, 2:26:33 AM

Confirmations

3,966,006

Merkle Root

d1504f35a90d2129bf9bcc5019308dc66a10f5c6c2ab656d36de6e97e3732807
Transactions (1)
Coinbased1504f35a90d21…de6e97e3732807
1 in β†’ 1 out7.3300 XPM110 B
AeRgRzDJ…zfvfzU2S
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.

5.427 Γ— 10⁹³(94-digit number)
54277814173635493931…50134997936245669920
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
5.427 Γ— 10⁹³(94-digit number)
54277814173635493931…50134997936245669921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.085 Γ— 10⁹⁴(95-digit number)
10855562834727098786…00269995872491339841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.171 Γ— 10⁹⁴(95-digit number)
21711125669454197572…00539991744982679681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.342 Γ— 10⁹⁴(95-digit number)
43422251338908395144…01079983489965359361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.684 Γ— 10⁹⁴(95-digit number)
86844502677816790289…02159966979930718721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.736 Γ— 10⁹⁡(96-digit number)
17368900535563358057…04319933959861437441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.473 Γ— 10⁹⁡(96-digit number)
34737801071126716115…08639867919722874881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.947 Γ— 10⁹⁡(96-digit number)
69475602142253432231…17279735839445749761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.389 Γ— 10⁹⁢(97-digit number)
13895120428450686446…34559471678891499521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.779 Γ— 10⁹⁢(97-digit number)
27790240856901372892…69118943357782999041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.558 Γ— 10⁹⁢(97-digit number)
55580481713802745785…38237886715565998081
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 2867681

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 42dc1a733ccd3fb50833c818a004acb32cc8053e141dfa42eb9da3414ee94601

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 #2,867,681 on Chainz β†—
Circulating Supply:57,913,716 XPMΒ·at block #6,833,686 Β· updates every 60s
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