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Home/Chain Registry/Block #2,099,736

Block #2,099,736

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2017, 4:56:40 PM Β· Difficulty 10.8562 Β· 4,743,232 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
077a49139c819848d0faa8757086309a2daf40ee43d072f137973f2389e88456
View on Chainz β†—

Difficulty

10.856229

Transactions

1

Size

200 B

Version

2

Bits

0adb31d0

Nonce

677,086,005

Timestamp

5/4/2017, 4:56:40 PM

Confirmations

4,743,232

Merkle Root

765d83f1e98e02d7d0292b0310d4185999aa373efd51cd537099fee4db8d24c9
Transactions (1)
Coinbase765d83f1e98e02…99fee4db8d24c9
1 in β†’ 1 out8.4700 XPM110 B
AS5g5iEb…Wb6tRmi4
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.

4.732 Γ— 10⁹⁴(95-digit number)
47328495146386613560…23334528734877863520
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
4.732 Γ— 10⁹⁴(95-digit number)
47328495146386613560…23334528734877863521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.465 Γ— 10⁹⁴(95-digit number)
94656990292773227121…46669057469755727041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.893 Γ— 10⁹⁡(96-digit number)
18931398058554645424…93338114939511454081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.786 Γ— 10⁹⁡(96-digit number)
37862796117109290848…86676229879022908161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.572 Γ— 10⁹⁡(96-digit number)
75725592234218581697…73352459758045816321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.514 Γ— 10⁹⁢(97-digit number)
15145118446843716339…46704919516091632641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.029 Γ— 10⁹⁢(97-digit number)
30290236893687432679…93409839032183265281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.058 Γ— 10⁹⁢(97-digit number)
60580473787374865358…86819678064366530561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.211 Γ— 10⁹⁷(98-digit number)
12116094757474973071…73639356128733061121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.423 Γ— 10⁹⁷(98-digit number)
24232189514949946143…47278712257466122241
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 2099736

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 077a49139c819848d0faa8757086309a2daf40ee43d072f137973f2389e88456

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 #2,099,736 on Chainz β†—
Circulating Supply:57,988,096 XPMΒ·at block #6,842,967 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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