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Block #1,435,241

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/29/2016, 8:07:17 PM Β· Difficulty 10.8113 Β· 5,405,148 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c42b366f6e3f875ef4f75fb3dd92c5c43eafe5dcfe47453e79147bacb1877e0c
View on Chainz β†—

Difficulty

10.811272

Transactions

1

Size

199 B

Version

2

Bits

0acfaf82

Nonce

1,514,747,728

Timestamp

1/29/2016, 8:07:17 PM

Confirmations

5,405,148

Merkle Root

8aa4a0e1deb63e8c38b50b26ee6a9f3a7b875eb652ee01329637556b5db75724
Transactions (1)
Coinbase8aa4a0e1deb63e…37556b5db75724
1 in β†’ 1 out8.5400 XPM109 B
APGB9yPd…Ew5mdKev
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.

3.883 Γ— 10⁹³(94-digit number)
38837898602860954734…34368961787120585920
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.883 Γ— 10⁹³(94-digit number)
38837898602860954734…34368961787120585919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.767 Γ— 10⁹³(94-digit number)
77675797205721909468…68737923574241171839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.553 Γ— 10⁹⁴(95-digit number)
15535159441144381893…37475847148482343679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.107 Γ— 10⁹⁴(95-digit number)
31070318882288763787…74951694296964687359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.214 Γ— 10⁹⁴(95-digit number)
62140637764577527575…49903388593929374719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.242 Γ— 10⁹⁡(96-digit number)
12428127552915505515…99806777187858749439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.485 Γ— 10⁹⁡(96-digit number)
24856255105831011030…99613554375717498879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.971 Γ— 10⁹⁡(96-digit number)
49712510211662022060…99227108751434997759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.942 Γ— 10⁹⁡(96-digit number)
99425020423324044120…98454217502869995519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.988 Γ— 10⁹⁢(97-digit number)
19885004084664808824…96908435005739991039
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 1435241

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 c42b366f6e3f875ef4f75fb3dd92c5c43eafe5dcfe47453e79147bacb1877e0c

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 #1,435,241 on Chainz β†—
Circulating Supply:57,967,434 XPMΒ·at block #6,840,388 Β· updates every 60s
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