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Home/Chain Registry/Block #1,681,483

Block #1,681,483

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 9:24:21 AM Β· Difficulty 10.7153 Β· 5,160,236 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1c9d1d9bf3b584375e7ea010217300574a8f5b9bbb7abf6dd17a91fcc1b754cc
View on Chainz β†—

Difficulty

10.715296

Transactions

1

Size

200 B

Version

2

Bits

0ab71da0

Nonce

271,100,455

Timestamp

7/20/2016, 9:24:21 AM

Confirmations

5,160,236

Merkle Root

fc029abf9995f6ed8251e3701836426f5d30530d17f021e05b1d533e8040282b
Transactions (1)
Coinbasefc029abf9995f6…1d533e8040282b
1 in β†’ 1 out8.7000 XPM110 B
AMJEfCa9…FUSqwSbv
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.

2.295 Γ— 10⁹⁡(96-digit number)
22957175535784871438…90785070278246999040
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
2.295 Γ— 10⁹⁡(96-digit number)
22957175535784871438…90785070278246999041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.591 Γ— 10⁹⁡(96-digit number)
45914351071569742877…81570140556493998081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.182 Γ— 10⁹⁡(96-digit number)
91828702143139485754…63140281112987996161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.836 Γ— 10⁹⁢(97-digit number)
18365740428627897150…26280562225975992321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.673 Γ— 10⁹⁢(97-digit number)
36731480857255794301…52561124451951984641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.346 Γ— 10⁹⁢(97-digit number)
73462961714511588603…05122248903903969281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.469 Γ— 10⁹⁷(98-digit number)
14692592342902317720…10244497807807938561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.938 Γ— 10⁹⁷(98-digit number)
29385184685804635441…20488995615615877121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.877 Γ— 10⁹⁷(98-digit number)
58770369371609270882…40977991231231754241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.175 Γ— 10⁹⁸(99-digit number)
11754073874321854176…81955982462463508481
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 1681483

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 1c9d1d9bf3b584375e7ea010217300574a8f5b9bbb7abf6dd17a91fcc1b754cc

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 #1,681,483 on Chainz β†—
Circulating Supply:57,978,133 XPMΒ·at block #6,841,718 Β· updates every 60s
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