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Home/Chain Registry/Block #2,651,445

Block #2,651,445

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2018, 8:08:45 PM Β· Difficulty 11.7508 Β· 4,190,056 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
662f00933851e91e0fc674c1e7b8a9314a6bcb48cc915e0364dc40c43b6ba120
View on Chainz β†—

Difficulty

11.750811

Transactions

1

Size

200 B

Version

2

Bits

0bc03523

Nonce

260,058,463

Timestamp

5/6/2018, 8:08:45 PM

Confirmations

4,190,056

Merkle Root

3f5a4391bd0d4dbdee2bd72042f3ee7dd059475b0b54e834be32fe1b2eda300e
Transactions (1)
Coinbase3f5a4391bd0d4d…32fe1b2eda300e
1 in β†’ 1 out7.2300 XPM110 B
ALAbFXK8…37ae4oPK
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.

1.526 Γ— 10⁹⁡(96-digit number)
15266724830475920481…53020900820778743200
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
1.526 Γ— 10⁹⁡(96-digit number)
15266724830475920481…53020900820778743201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.053 Γ— 10⁹⁡(96-digit number)
30533449660951840962…06041801641557486401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.106 Γ— 10⁹⁡(96-digit number)
61066899321903681924…12083603283114972801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.221 Γ— 10⁹⁢(97-digit number)
12213379864380736384…24167206566229945601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.442 Γ— 10⁹⁢(97-digit number)
24426759728761472769…48334413132459891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.885 Γ— 10⁹⁢(97-digit number)
48853519457522945539…96668826264919782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.770 Γ— 10⁹⁢(97-digit number)
97707038915045891078…93337652529839564801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.954 Γ— 10⁹⁷(98-digit number)
19541407783009178215…86675305059679129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.908 Γ— 10⁹⁷(98-digit number)
39082815566018356431…73350610119358259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.816 Γ— 10⁹⁷(98-digit number)
78165631132036712862…46701220238716518401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.563 Γ— 10⁹⁸(99-digit number)
15633126226407342572…93402440477433036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
3.126 Γ— 10⁹⁸(99-digit number)
31266252452814685145…86804880954866073601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2651445

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 662f00933851e91e0fc674c1e7b8a9314a6bcb48cc915e0364dc40c43b6ba120

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 #2,651,445 on Chainz β†—
Circulating Supply:57,976,386 XPMΒ·at block #6,841,500 Β· updates every 60s
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