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Home/Chain Registry/Block #2,634,020

Block #2,634,020

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 5:38:17 PM Β· Difficulty 11.2184 Β· 4,204,738 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ab3b2282abb7dd79ab89f4071d23c3d0c06bcdace5fb3db6dcb987e663299087
View on Chainz β†—

Difficulty

11.218361

Transactions

2

Size

428 B

Version

2

Bits

0b37e67d

Nonce

586,486,687

Timestamp

4/28/2018, 5:38:17 PM

Confirmations

4,204,738

Merkle Root

bafce1bbe85593ca257b25d070378decc015336dbf2d320a8161061c7ce45c5e
Transactions (2)
Coinbase1b775f6b5c7cf8…2971a922e4b065
1 in β†’ 1 out7.9400 XPM110 B
AZsQ7oY8…mekrgcjN
7d3d6d25ecb0f3…f9d72fcfaef121
1 in β†’ 2 out375.2750 XPM227 B
AeqJc9MU…KF4wwYn5Aa5dSchn…4fSKsK68
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.

5.639 Γ— 10⁹⁷(98-digit number)
56393117241224337885…62865008700426158080
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
5.639 Γ— 10⁹⁷(98-digit number)
56393117241224337885…62865008700426158081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.127 Γ— 10⁹⁸(99-digit number)
11278623448244867577…25730017400852316161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.255 Γ— 10⁹⁸(99-digit number)
22557246896489735154…51460034801704632321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.511 Γ— 10⁹⁸(99-digit number)
45114493792979470308…02920069603409264641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.022 Γ— 10⁹⁸(99-digit number)
90228987585958940617…05840139206818529281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.804 Γ— 10⁹⁹(100-digit number)
18045797517191788123…11680278413637058561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.609 Γ— 10⁹⁹(100-digit number)
36091595034383576246…23360556827274117121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.218 Γ— 10⁹⁹(100-digit number)
72183190068767152493…46721113654548234241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.443 Γ— 10¹⁰⁰(101-digit number)
14436638013753430498…93442227309096468481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.887 Γ— 10¹⁰⁰(101-digit number)
28873276027506860997…86884454618192936961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.774 Γ— 10¹⁰⁰(101-digit number)
57746552055013721995…73768909236385873921
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 2634020

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 ab3b2282abb7dd79ab89f4071d23c3d0c06bcdace5fb3db6dcb987e663299087

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 #2,634,020 on Chainz β†—
Circulating Supply:57,954,321 XPMΒ·at block #6,838,757 Β· updates every 60s
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