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Home/Chain Registry/Block #1,693,748

Block #1,693,748

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/29/2016, 8:08:10 AM Β· Difficulty 10.6786 Β· 5,132,876 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
60698216e61a29138222a6dcfc097b05fbd921dfdfd366dd46dd0fa5e4d41dff
View on Chainz β†—

Difficulty

10.678564

Transactions

1

Size

200 B

Version

2

Bits

0aadb65a

Nonce

782,089,964

Timestamp

7/29/2016, 8:08:10 AM

Confirmations

5,132,876

Merkle Root

c271c2bcc9dbaab39012db7e79e78664d8e82177b7143488e6ab39e58dbc7a77
Transactions (1)
Coinbasec271c2bcc9dbaa…ab39e58dbc7a77
1 in β†’ 1 out8.7600 XPM109 B
APyw9UU6…WoJBz4Ek
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.

3.305 Γ— 10⁹⁷(98-digit number)
33050104812926117049…93315748220646195200
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
3.305 Γ— 10⁹⁷(98-digit number)
33050104812926117049…93315748220646195199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.610 Γ— 10⁹⁷(98-digit number)
66100209625852234099…86631496441292390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.322 Γ— 10⁹⁸(99-digit number)
13220041925170446819…73262992882584780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.644 Γ— 10⁹⁸(99-digit number)
26440083850340893639…46525985765169561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.288 Γ— 10⁹⁸(99-digit number)
52880167700681787279…93051971530339123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.057 Γ— 10⁹⁹(100-digit number)
10576033540136357455…86103943060678246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.115 Γ— 10⁹⁹(100-digit number)
21152067080272714911…72207886121356492799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.230 Γ— 10⁹⁹(100-digit number)
42304134160545429823…44415772242712985599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.460 Γ— 10⁹⁹(100-digit number)
84608268321090859647…88831544485425971199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.692 Γ— 10¹⁰⁰(101-digit number)
16921653664218171929…77663088970851942399
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 1693748

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 60698216e61a29138222a6dcfc097b05fbd921dfdfd366dd46dd0fa5e4d41dff

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 #1,693,748 on Chainz β†—
Circulating Supply:57,857,146 XPMΒ·at block #6,826,623 Β· updates every 60s
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