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Home/Chain Registry/Block #1,991,046

Block #1,991,046

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/20/2017, 6:42:21 AM Β· Difficulty 10.7344 Β· 4,835,965 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
08dd376a7575323f748ef35e602753dc325694673b8f202e2afc0ef6923c11e7
View on Chainz β†—

Difficulty

10.734403

Transactions

1

Size

199 B

Version

2

Bits

0abc01ce

Nonce

313,054,430

Timestamp

2/20/2017, 6:42:21 AM

Confirmations

4,835,965

Merkle Root

7c33f899c14bbaaf8b089aad1c8c0d3918d6d7691a08d30b570964f4ed9b31df
Transactions (1)
Coinbase7c33f899c14bba…0964f4ed9b31df
1 in β†’ 1 out8.6600 XPM109 B
AUV5gpaQ…7BreWt8V
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.

4.868 Γ— 10⁹⁡(96-digit number)
48687344360547617713…85063157391267067520
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
4.868 Γ— 10⁹⁡(96-digit number)
48687344360547617713…85063157391267067521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.737 Γ— 10⁹⁡(96-digit number)
97374688721095235426…70126314782534135041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.947 Γ— 10⁹⁢(97-digit number)
19474937744219047085…40252629565068270081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.894 Γ— 10⁹⁢(97-digit number)
38949875488438094170…80505259130136540161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.789 Γ— 10⁹⁢(97-digit number)
77899750976876188341…61010518260273080321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.557 Γ— 10⁹⁷(98-digit number)
15579950195375237668…22021036520546160641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.115 Γ— 10⁹⁷(98-digit number)
31159900390750475336…44042073041092321281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.231 Γ— 10⁹⁷(98-digit number)
62319800781500950673…88084146082184642561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.246 Γ— 10⁹⁸(99-digit number)
12463960156300190134…76168292164369285121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.492 Γ— 10⁹⁸(99-digit number)
24927920312600380269…52336584328738570241
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 1991046

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 08dd376a7575323f748ef35e602753dc325694673b8f202e2afc0ef6923c11e7

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 #1,991,046 on Chainz β†—
Circulating Supply:57,860,265 XPMΒ·at block #6,827,010 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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