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Block #2,645,580

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 11:32:43 PM Β· Difficulty 11.7349 Β· 4,187,057 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
68d49bfa3b79a7442f7a8afd82346b424c4413cf2251998f7a0fc86e46611e49
View on Chainz β†—

Difficulty

11.734850

Transactions

2

Size

427 B

Version

2

Bits

0bbc1f23

Nonce

186,781,147

Timestamp

5/2/2018, 11:32:43 PM

Confirmations

4,187,057

Merkle Root

5e24084a8753916c79aa1a41782fc2346b65580495936048a5a79237e2329c1b
Transactions (2)
Coinbase2cd1075ad30f97…512ac1280a6d4c
1 in β†’ 1 out7.2600 XPM110 B
AbaNmNrx…1QDtHC5h
323883cd5b0406…2733a12b817f2b
1 in β†’ 2 out299.9900 XPM227 B
AbV3zhhR…Re4sLygeAbf5xqEx…ADagQxez
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— 10⁹⁴(95-digit number)
18540656179876274835…29617789788940907960
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— 10⁹⁴(95-digit number)
18540656179876274835…29617789788940907961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.708 Γ— 10⁹⁴(95-digit number)
37081312359752549670…59235579577881815921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.416 Γ— 10⁹⁴(95-digit number)
74162624719505099341…18471159155763631841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.483 Γ— 10⁹⁡(96-digit number)
14832524943901019868…36942318311527263681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.966 Γ— 10⁹⁡(96-digit number)
29665049887802039736…73884636623054527361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.933 Γ— 10⁹⁡(96-digit number)
59330099775604079473…47769273246109054721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.186 Γ— 10⁹⁢(97-digit number)
11866019955120815894…95538546492218109441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.373 Γ— 10⁹⁢(97-digit number)
23732039910241631789…91077092984436218881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.746 Γ— 10⁹⁢(97-digit number)
47464079820483263578…82154185968872437761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.492 Γ— 10⁹⁢(97-digit number)
94928159640966527157…64308371937744875521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.898 Γ— 10⁹⁷(98-digit number)
18985631928193305431…28616743875489751041
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 2645580

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 68d49bfa3b79a7442f7a8afd82346b424c4413cf2251998f7a0fc86e46611e49

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 #2,645,580 on Chainz β†—
Circulating Supply:57,905,245 XPMΒ·at block #6,832,636 Β· updates every 60s
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