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Home/Chain Registry/Block #2,699,098

Block #2,699,098

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/10/2018, 4:26:00 AM Β· Difficulty 11.6455 Β· 4,133,308 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
81734f9f08f4a69cb0dc6e6d8e768f24d618bb7e44f0bc343590c65d7ae22684
View on Chainz β†—

Difficulty

11.645483

Transactions

1

Size

199 B

Version

2

Bits

0ba53e5d

Nonce

1,798,490,535

Timestamp

6/10/2018, 4:26:00 AM

Confirmations

4,133,308

Merkle Root

1cf006ba13a74fd4a8b6feab40d231d2256ddaee370f6d4b7ef7cb9f6c837241
Transactions (1)
Coinbase1cf006ba13a74f…f7cb9f6c837241
1 in β†’ 1 out7.3600 XPM109 B
AYJLpD8f…oxr6gVn2
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.

6.061 Γ— 10⁹⁡(96-digit number)
60612401811851363435…01518174811737299360
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
6.061 Γ— 10⁹⁡(96-digit number)
60612401811851363435…01518174811737299361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.212 Γ— 10⁹⁢(97-digit number)
12122480362370272687…03036349623474598721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.424 Γ— 10⁹⁢(97-digit number)
24244960724740545374…06072699246949197441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.848 Γ— 10⁹⁢(97-digit number)
48489921449481090748…12145398493898394881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.697 Γ— 10⁹⁢(97-digit number)
96979842898962181496…24290796987796789761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.939 Γ— 10⁹⁷(98-digit number)
19395968579792436299…48581593975593579521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.879 Γ— 10⁹⁷(98-digit number)
38791937159584872598…97163187951187159041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.758 Γ— 10⁹⁷(98-digit number)
77583874319169745197…94326375902374318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.551 Γ— 10⁹⁸(99-digit number)
15516774863833949039…88652751804748636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.103 Γ— 10⁹⁸(99-digit number)
31033549727667898078…77305503609497272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.206 Γ— 10⁹⁸(99-digit number)
62067099455335796157…54611007218994544641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2699098

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 81734f9f08f4a69cb0dc6e6d8e768f24d618bb7e44f0bc343590c65d7ae22684

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 #2,699,098 on Chainz β†—
Circulating Supply:57,903,393 XPMΒ·at block #6,832,405 Β· updates every 60s
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