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Home/Chain Registry/Block #2,100,499

Block #2,100,499

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2017, 6:06:12 AM Β· Difficulty 10.8555 Β· 4,740,414 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c5d3039a8da4a4de47cc883e8d46a0e0a6340ff20dc98bd7192a1a1f5cd99f60
View on Chainz β†—

Difficulty

10.855504

Transactions

1

Size

199 B

Version

2

Bits

0adb0249

Nonce

442,880,425

Timestamp

5/5/2017, 6:06:12 AM

Confirmations

4,740,414

Merkle Root

b265c01433e88a91b74ee2e72987d0dc7c9e0d128209830b62a214d31cddfe26
Transactions (1)
Coinbaseb265c01433e88a…a214d31cddfe26
1 in β†’ 1 out8.4700 XPM109 B
AP5e3CZB…mnqYtvfr
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.

6.235 Γ— 10⁹³(94-digit number)
62359250880623175558…21121465159381393440
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
6.235 Γ— 10⁹³(94-digit number)
62359250880623175558…21121465159381393441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.247 Γ— 10⁹⁴(95-digit number)
12471850176124635111…42242930318762786881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.494 Γ— 10⁹⁴(95-digit number)
24943700352249270223…84485860637525573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.988 Γ— 10⁹⁴(95-digit number)
49887400704498540446…68971721275051147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.977 Γ— 10⁹⁴(95-digit number)
99774801408997080892…37943442550102295041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.995 Γ— 10⁹⁡(96-digit number)
19954960281799416178…75886885100204590081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.990 Γ— 10⁹⁡(96-digit number)
39909920563598832357…51773770200409180161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.981 Γ— 10⁹⁡(96-digit number)
79819841127197664714…03547540400818360321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.596 Γ— 10⁹⁢(97-digit number)
15963968225439532942…07095080801636720641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.192 Γ— 10⁹⁢(97-digit number)
31927936450879065885…14190161603273441281
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 2100499

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 c5d3039a8da4a4de47cc883e8d46a0e0a6340ff20dc98bd7192a1a1f5cd99f60

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 #2,100,499 on Chainz β†—
Circulating Supply:57,971,654 XPMΒ·at block #6,840,912 Β· updates every 60s
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