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Home/Chain Registry/Block #1,662,207

Block #1,662,207

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/6/2016, 7:21:52 PM Β· Difficulty 10.7303 Β· 5,182,583 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7996b6ba72a65a42168dee428db9ba80edafe7fccd0e193d65c0843814f08a93
View on Chainz β†—

Difficulty

10.730309

Transactions

1

Size

243 B

Version

2

Bits

0abaf582

Nonce

22,583,875

Timestamp

7/6/2016, 7:21:52 PM

Confirmations

5,182,583

Merkle Root

8e9fac1549751eb92ab8c120283bbc83d80036e9695df36a077ddb7e011aab2d
Transactions (1)
Coinbase8e9fac1549751e…7ddb7e011aab2d
1 in β†’ 2 out8.6700 XPM152 B
ARf92pmr…CsyVkynHALPu3s2c…EJXLjVFh
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.

4.237 Γ— 10⁹⁢(97-digit number)
42372375949890109954…45419557673347351360
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
4.237 Γ— 10⁹⁢(97-digit number)
42372375949890109954…45419557673347351361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.474 Γ— 10⁹⁢(97-digit number)
84744751899780219908…90839115346694702721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.694 Γ— 10⁹⁷(98-digit number)
16948950379956043981…81678230693389405441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.389 Γ— 10⁹⁷(98-digit number)
33897900759912087963…63356461386778810881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.779 Γ— 10⁹⁷(98-digit number)
67795801519824175926…26712922773557621761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.355 Γ— 10⁹⁸(99-digit number)
13559160303964835185…53425845547115243521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.711 Γ— 10⁹⁸(99-digit number)
27118320607929670370…06851691094230487041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.423 Γ— 10⁹⁸(99-digit number)
54236641215859340741…13703382188460974081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.084 Γ— 10⁹⁹(100-digit number)
10847328243171868148…27406764376921948161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.169 Γ— 10⁹⁹(100-digit number)
21694656486343736296…54813528753843896321
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 1662207

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 7996b6ba72a65a42168dee428db9ba80edafe7fccd0e193d65c0843814f08a93

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 #1,662,207 on Chainz β†—
Circulating Supply:58,002,733 XPMΒ·at block #6,844,789 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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