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Home/Chain Registry/Block #2,640,981

Block #2,640,981

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 4:56:06 AM Β· Difficulty 11.6022 Β· 4,199,312 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f789a02158675745dc9bb634f68c6b097b46c7dd0b9440ee375781ddbe3b5fc
View on Chainz β†—

Difficulty

11.602193

Transactions

1

Size

200 B

Version

2

Bits

0b9a2955

Nonce

864,584,927

Timestamp

5/1/2018, 4:56:06 AM

Confirmations

4,199,312

Merkle Root

0e3fa90db3fbca43d4385b591e00e4510a7a32535603a1a62865a1a2c3a74f4c
Transactions (1)
Coinbase0e3fa90db3fbca…65a1a2c3a74f4c
1 in β†’ 1 out7.4200 XPM110 B
AVsMtkfC…j3aoVjj9
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.

6.187 Γ— 10⁹³(94-digit number)
61874286034144033411…28867911489390862800
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
6.187 Γ— 10⁹³(94-digit number)
61874286034144033411…28867911489390862801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.237 Γ— 10⁹⁴(95-digit number)
12374857206828806682…57735822978781725601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.474 Γ— 10⁹⁴(95-digit number)
24749714413657613364…15471645957563451201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.949 Γ— 10⁹⁴(95-digit number)
49499428827315226729…30943291915126902401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.899 Γ— 10⁹⁴(95-digit number)
98998857654630453458…61886583830253804801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.979 Γ— 10⁹⁡(96-digit number)
19799771530926090691…23773167660507609601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.959 Γ— 10⁹⁡(96-digit number)
39599543061852181383…47546335321015219201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.919 Γ— 10⁹⁡(96-digit number)
79199086123704362766…95092670642030438401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.583 Γ— 10⁹⁢(97-digit number)
15839817224740872553…90185341284060876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.167 Γ— 10⁹⁢(97-digit number)
31679634449481745106…80370682568121753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.335 Γ— 10⁹⁢(97-digit number)
63359268898963490213…60741365136243507201
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 2640981

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 3f789a02158675745dc9bb634f68c6b097b46c7dd0b9440ee375781ddbe3b5fc

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 #2,640,981 on Chainz β†—
Circulating Supply:57,966,662 XPMΒ·at block #6,840,292 Β· updates every 60s
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