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Block #842,520

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/6/2014, 5:02:01 PM Β· Difficulty 10.9736 Β· 5,998,097 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5e95d93a80b6048f1be4da0e2ca897d0103511e0e8be2ab5ede72a3409c89cbf
View on Chainz β†—

Height

#842,520

Difficulty

10.973577

Transactions

2

Size

433 B

Version

2

Bits

0af93c54

Nonce

1,637,652,519

Timestamp

12/6/2014, 5:02:01 PM

Confirmations

5,998,097

Merkle Root

fd088d76c3603348d4dacda694e9319ce03fa273ae2af1f62c7a004b539d44bd
Transactions (2)
Coinbasecece5ac113f1cb…5feeeb02c182f0
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
31044c3d73f623…7de6d4fa8d5ae3
1 in β†’ 2 out0.5708 XPM226 B
AL67V7Bz…GYhsxKLLAHg6GYJ2…Axatqine
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.

4.274 Γ— 10⁹⁷(98-digit number)
42747947457373383124…95222892525795624960
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
4.274 Γ— 10⁹⁷(98-digit number)
42747947457373383124…95222892525795624961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.549 Γ— 10⁹⁷(98-digit number)
85495894914746766248…90445785051591249921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.709 Γ— 10⁹⁸(99-digit number)
17099178982949353249…80891570103182499841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.419 Γ— 10⁹⁸(99-digit number)
34198357965898706499…61783140206364999681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.839 Γ— 10⁹⁸(99-digit number)
68396715931797412999…23566280412729999361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.367 Γ— 10⁹⁹(100-digit number)
13679343186359482599…47132560825459998721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.735 Γ— 10⁹⁹(100-digit number)
27358686372718965199…94265121650919997441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.471 Γ— 10⁹⁹(100-digit number)
54717372745437930399…88530243301839994881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.094 Γ— 10¹⁰⁰(101-digit number)
10943474549087586079…77060486603679989761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.188 Γ— 10¹⁰⁰(101-digit number)
21886949098175172159…54120973207359979521
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 842520

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 5e95d93a80b6048f1be4da0e2ca897d0103511e0e8be2ab5ede72a3409c89cbf

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 #842,520 on Chainz β†—
Circulating Supply:57,969,274 XPMΒ·at block #6,840,616 Β· updates every 60s
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