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Home/Chain Registry/Block #1,542,699

Block #1,542,699

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/15/2016, 4:25:09 PM Β· Difficulty 10.6493 Β· 5,284,664 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67e23b59af304d8a349ad37498da362fa05edbbc3100fdc8f5c08240dd0e2b35
View on Chainz β†—

Difficulty

10.649283

Transactions

1

Size

199 B

Version

2

Bits

0aa63771

Nonce

361,279,075

Timestamp

4/15/2016, 4:25:09 PM

Confirmations

5,284,664

Merkle Root

b37d4f26617212fb814b82c894e3e8d9e45948a9ea4f20563d85239454a6b06a
Transactions (1)
Coinbaseb37d4f26617212…85239454a6b06a
1 in β†’ 1 out8.8000 XPM109 B
AQWEsi2X…scPjxJRW
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.

3.708 Γ— 10⁹³(94-digit number)
37085980408900786570…84594733565408731200
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
3.708 Γ— 10⁹³(94-digit number)
37085980408900786570…84594733565408731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.417 Γ— 10⁹³(94-digit number)
74171960817801573140…69189467130817462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.483 Γ— 10⁹⁴(95-digit number)
14834392163560314628…38378934261634924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.966 Γ— 10⁹⁴(95-digit number)
29668784327120629256…76757868523269849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.933 Γ— 10⁹⁴(95-digit number)
59337568654241258512…53515737046539699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.186 Γ— 10⁹⁡(96-digit number)
11867513730848251702…07031474093079398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.373 Γ— 10⁹⁡(96-digit number)
23735027461696503404…14062948186158796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.747 Γ— 10⁹⁡(96-digit number)
47470054923393006809…28125896372317593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.494 Γ— 10⁹⁡(96-digit number)
94940109846786013619…56251792744635187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.898 Γ— 10⁹⁢(97-digit number)
18988021969357202723…12503585489270374401
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 1542699

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 67e23b59af304d8a349ad37498da362fa05edbbc3100fdc8f5c08240dd0e2b35

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 #1,542,699 on Chainz β†—
Circulating Supply:57,863,004 XPMΒ·at block #6,827,362 Β· updates every 60s
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