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Home/Chain Registry/Block #2,103,599

Block #2,103,599

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2017, 9:12:02 PM Β· Difficulty 10.8757 Β· 4,729,818 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bea30ede20f5f7c1b30cae6f9b379ef4e1518c12965d642bd567891bbee181b8
View on Chainz β†—

Difficulty

10.875678

Transactions

1

Size

198 B

Version

2

Bits

0ae02c75

Nonce

1,405,621,464

Timestamp

5/6/2017, 9:12:02 PM

Confirmations

4,729,818

Merkle Root

bc672a3c904ca2fb9300f27f0c7fd471cec2873225da2aac8425f52502040dfe
Transactions (1)
Coinbasebc672a3c904ca2…25f52502040dfe
1 in β†’ 1 out8.4400 XPM109 B
AVsb77ta…ty6zVjza
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.

1.854 Γ— 10⁹³(94-digit number)
18548609252430900392…37562050238278688000
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
1.854 Γ— 10⁹³(94-digit number)
18548609252430900392…37562050238278688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.709 Γ— 10⁹³(94-digit number)
37097218504861800785…75124100476557376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.419 Γ— 10⁹³(94-digit number)
74194437009723601570…50248200953114752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.483 Γ— 10⁹⁴(95-digit number)
14838887401944720314…00496401906229504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.967 Γ— 10⁹⁴(95-digit number)
29677774803889440628…00992803812459008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.935 Γ— 10⁹⁴(95-digit number)
59355549607778881256…01985607624918016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.187 Γ— 10⁹⁡(96-digit number)
11871109921555776251…03971215249836032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.374 Γ— 10⁹⁡(96-digit number)
23742219843111552502…07942430499672064001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.748 Γ— 10⁹⁡(96-digit number)
47484439686223105005…15884860999344128001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.496 Γ— 10⁹⁡(96-digit number)
94968879372446210010…31769721998688256001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.899 Γ— 10⁹⁢(97-digit number)
18993775874489242002…63539443997376512001
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 2103599

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 bea30ede20f5f7c1b30cae6f9b379ef4e1518c12965d642bd567891bbee181b8

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 #2,103,599 on Chainz β†—
Circulating Supply:57,911,538 XPMΒ·at block #6,833,416 Β· updates every 60s
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