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Home/Chain Registry/Block #2,242,045

Block #2,242,045

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2017, 5:41:54 AM Β· Difficulty 10.9472 Β· 4,596,018 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67c64a50f4dc5204dfdc0d4a2e0b0372f3a991732d4032271a472a7d6871f4a0
View on Chainz β†—

Difficulty

10.947235

Transactions

2

Size

722 B

Version

2

Bits

0af27df8

Nonce

595,318,900

Timestamp

8/8/2017, 5:41:54 AM

Confirmations

4,596,018

Merkle Root

7fb433b586a992bf6e65ce25342b50826794352b2ca3972b553fb8f7119f2611
Transactions (2)
Coinbase7ffd75038e3709…622825d3120c82
1 in β†’ 1 out8.3400 XPM109 B
AZnN1Dve…VX8TpZSS
be4a823d54c6d9…5511e0757a19af
3 in β†’ 2 out164.0550 XPM523 B
AYM2MmJf…UqRvHtSuAd27Nz4m…CCnTdvs6
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.

5.850 Γ— 10⁹⁡(96-digit number)
58509786480489841819…70841742519041036800
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
5.850 Γ— 10⁹⁡(96-digit number)
58509786480489841819…70841742519041036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.170 Γ— 10⁹⁢(97-digit number)
11701957296097968363…41683485038082073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.340 Γ— 10⁹⁢(97-digit number)
23403914592195936727…83366970076164147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.680 Γ— 10⁹⁢(97-digit number)
46807829184391873455…66733940152328294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.361 Γ— 10⁹⁢(97-digit number)
93615658368783746911…33467880304656588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.872 Γ— 10⁹⁷(98-digit number)
18723131673756749382…66935760609313177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.744 Γ— 10⁹⁷(98-digit number)
37446263347513498764…33871521218626355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.489 Γ— 10⁹⁷(98-digit number)
74892526695026997529…67743042437252710401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.497 Γ— 10⁹⁸(99-digit number)
14978505339005399505…35486084874505420801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.995 Γ— 10⁹⁸(99-digit number)
29957010678010799011…70972169749010841601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2242045

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 67c64a50f4dc5204dfdc0d4a2e0b0372f3a991732d4032271a472a7d6871f4a0

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 #2,242,045 on Chainz β†—
Circulating Supply:57,948,860 XPMΒ·at block #6,838,062 Β· updates every 60s
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