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Block #714,031

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2014, 5:47:46 PM Β· Difficulty 10.9555 Β· 6,086,184 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2a113c48e9d524b82dcbb7f0e238dc6d82fca3e7b9e835640f1bdfb8ca6bf310
View on Chainz β†—

Height

#714,031

Difficulty

10.955547

Transactions

2

Size

21.67 KB

Version

2

Bits

0af49ebf

Nonce

45,979,585

Timestamp

9/9/2014, 5:47:46 PM

Confirmations

6,086,184

Merkle Root

d52433b9fec9e36456e8c577d211388935b3f8ebc279ac96d32a665ecfca729a
Transactions (2)
Coinbase77e185df32712c…317861d0e2888b
1 in β†’ 1 out8.5400 XPM116 B
ANSXnLY2…Sd25TjkD
f53672dbdbc935…604ec83c1dd879
148 in β†’ 2 out451.8923 XPM21.47 KB
APs1YyQX…R2zQQ7ojAUoz9UQ6…5WQmZSrH
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.

1.039 Γ— 10⁹⁸(99-digit number)
10398960404772063840…75460505797899960320
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
1.039 Γ— 10⁹⁸(99-digit number)
10398960404772063840…75460505797899960319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.079 Γ— 10⁹⁸(99-digit number)
20797920809544127680…50921011595799920639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.159 Γ— 10⁹⁸(99-digit number)
41595841619088255361…01842023191599841279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.319 Γ— 10⁹⁸(99-digit number)
83191683238176510722…03684046383199682559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.663 Γ— 10⁹⁹(100-digit number)
16638336647635302144…07368092766399365119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.327 Γ— 10⁹⁹(100-digit number)
33276673295270604289…14736185532798730239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.655 Γ— 10⁹⁹(100-digit number)
66553346590541208578…29472371065597460479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.331 Γ— 10¹⁰⁰(101-digit number)
13310669318108241715…58944742131194920959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.662 Γ— 10¹⁰⁰(101-digit number)
26621338636216483431…17889484262389841919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.324 Γ— 10¹⁰⁰(101-digit number)
53242677272432966862…35778968524779683839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.064 Γ— 10¹⁰¹(102-digit number)
10648535454486593372…71557937049559367679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 714031

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 2a113c48e9d524b82dcbb7f0e238dc6d82fca3e7b9e835640f1bdfb8ca6bf310

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 #714,031 on Chainz β†—
Circulating Supply:57,645,771 XPMΒ·at block #6,800,214 Β· updates every 60s
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