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Home/Chain Registry/Block #2,468,616

Block #2,468,616

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/11/2018, 10:55:32 PM Β· Difficulty 10.9601 Β· 4,374,607 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e82f1b87ac22bdb5deb9c804aa0a6f051f2cd84b65dba5442e283cb084c4fcf7
View on Chainz β†—

Difficulty

10.960061

Transactions

2

Size

574 B

Version

2

Bits

0af5c68d

Nonce

1,678,846,840

Timestamp

1/11/2018, 10:55:32 PM

Confirmations

4,374,607

Merkle Root

7e6cd0ba40a560595af596b282dd9893d8c47fe6a21869294e505aa1d08cc8af
Transactions (2)
Coinbase27b38c6fee3220…ad3456849ae8d3
1 in β†’ 1 out8.3300 XPM109 B
ASAQw5EJ…tHa3AhLY
3aa7ef17da0fec…92ac3d73fec83f
2 in β†’ 2 out148.1297 XPM374 B
AVss7v2D…omsyYryVASGWZaQ6…ZrEN4hgn
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.

6.602 Γ— 10⁹⁢(97-digit number)
66021478512987312337…14268534296415027200
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
6.602 Γ— 10⁹⁢(97-digit number)
66021478512987312337…14268534296415027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.320 Γ— 10⁹⁷(98-digit number)
13204295702597462467…28537068592830054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.640 Γ— 10⁹⁷(98-digit number)
26408591405194924934…57074137185660108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.281 Γ— 10⁹⁷(98-digit number)
52817182810389849869…14148274371320217601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.056 Γ— 10⁹⁸(99-digit number)
10563436562077969973…28296548742640435201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.112 Γ— 10⁹⁸(99-digit number)
21126873124155939947…56593097485280870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.225 Γ— 10⁹⁸(99-digit number)
42253746248311879895…13186194970561740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.450 Γ— 10⁹⁸(99-digit number)
84507492496623759791…26372389941123481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.690 Γ— 10⁹⁹(100-digit number)
16901498499324751958…52744779882246963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.380 Γ— 10⁹⁹(100-digit number)
33802996998649503916…05489559764493926401
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 2468616

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 e82f1b87ac22bdb5deb9c804aa0a6f051f2cd84b65dba5442e283cb084c4fcf7

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 #2,468,616 on Chainz β†—
Circulating Supply:57,990,158 XPMΒ·at block #6,843,222 Β· updates every 60s
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