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Home/Chain Registry/Block #2,721,774

Block #2,721,774

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/26/2018, 5:34:19 AM Β· Difficulty 11.6145 Β· 4,121,193 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bea6ed1c8f8ee83e9bfe54ea74842c8f3157542ec1778ca39eafeff126275c0e
View on Chainz β†—

Difficulty

11.614545

Transactions

1

Size

200 B

Version

2

Bits

0b9d52d2

Nonce

275,578,610

Timestamp

6/26/2018, 5:34:19 AM

Confirmations

4,121,193

Merkle Root

bc8bbe1ec8dc1562e161ee59375127a760be10e62fbb4182ff827812ec77cbc3
Transactions (1)
Coinbasebc8bbe1ec8dc15…827812ec77cbc3
1 in β†’ 1 out7.4000 XPM109 B
AbWDYYUZ…Aoy4UqHk
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.

8.459 Γ— 10⁹⁡(96-digit number)
84599954528321729675…96316534105855126080
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
8.459 Γ— 10⁹⁡(96-digit number)
84599954528321729675…96316534105855126081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.691 Γ— 10⁹⁢(97-digit number)
16919990905664345935…92633068211710252161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.383 Γ— 10⁹⁢(97-digit number)
33839981811328691870…85266136423420504321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.767 Γ— 10⁹⁢(97-digit number)
67679963622657383740…70532272846841008641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.353 Γ— 10⁹⁷(98-digit number)
13535992724531476748…41064545693682017281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.707 Γ— 10⁹⁷(98-digit number)
27071985449062953496…82129091387364034561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.414 Γ— 10⁹⁷(98-digit number)
54143970898125906992…64258182774728069121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.082 Γ— 10⁹⁸(99-digit number)
10828794179625181398…28516365549456138241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.165 Γ— 10⁹⁸(99-digit number)
21657588359250362796…57032731098912276481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.331 Γ— 10⁹⁸(99-digit number)
43315176718500725593…14065462197824552961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.663 Γ— 10⁹⁸(99-digit number)
86630353437001451187…28130924395649105921
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 2721774

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 bea6ed1c8f8ee83e9bfe54ea74842c8f3157542ec1778ca39eafeff126275c0e

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 #2,721,774 on Chainz β†—
Circulating Supply:57,988,088 XPMΒ·at block #6,842,966 Β· updates every 60s
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