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Home/Chain Registry/Block #2,639,022

Block #2,639,022

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 12:16:04 PM Β· Difficulty 11.5188 Β· 4,197,430 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
166bb417b08fb5241408e9af6adb49184fb827a4ab63b02a37e2a989ed690e42
View on Chainz β†—

Difficulty

11.518781

Transactions

2

Size

724 B

Version

2

Bits

0b84ced8

Nonce

567,778,859

Timestamp

4/30/2018, 12:16:04 PM

Confirmations

4,197,430

Merkle Root

4ab91e848b6c155f704eb96a9feeca517567ff4da749f1ef95edf391d2e31049
Transactions (2)
Coinbase4fbb0809ffca27…04fda6eb8d719a
1 in β†’ 1 out7.5300 XPM110 B
AXcUCV4T…oyzGcWcx
c3f48ef2c1360c…84a7b295e439b2
3 in β†’ 2 out465.0100 XPM524 B
ANSt9ABz…2J5riagjALq3a8dg…i8S8c1TT
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.

9.665 Γ— 10⁹³(94-digit number)
96655819747722161141…50183903662477980160
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
9.665 Γ— 10⁹³(94-digit number)
96655819747722161141…50183903662477980161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.933 Γ— 10⁹⁴(95-digit number)
19331163949544432228…00367807324955960321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.866 Γ— 10⁹⁴(95-digit number)
38662327899088864456…00735614649911920641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.732 Γ— 10⁹⁴(95-digit number)
77324655798177728913…01471229299823841281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.546 Γ— 10⁹⁡(96-digit number)
15464931159635545782…02942458599647682561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.092 Γ— 10⁹⁡(96-digit number)
30929862319271091565…05884917199295365121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.185 Γ— 10⁹⁡(96-digit number)
61859724638542183130…11769834398590730241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.237 Γ— 10⁹⁢(97-digit number)
12371944927708436626…23539668797181460481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.474 Γ— 10⁹⁢(97-digit number)
24743889855416873252…47079337594362920961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.948 Γ— 10⁹⁢(97-digit number)
49487779710833746504…94158675188725841921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.897 Γ— 10⁹⁢(97-digit number)
98975559421667493008…88317350377451683841
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 2639022

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 166bb417b08fb5241408e9af6adb49184fb827a4ab63b02a37e2a989ed690e42

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 #2,639,022 on Chainz β†—
Circulating Supply:57,935,887 XPMΒ·at block #6,836,451 Β· updates every 60s
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