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Home/Chain Registry/Block #784,277

Block #784,277

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/26/2014, 6:46:56 PM Β· Difficulty 10.9751 Β· 6,016,576 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab81f489dfbd8d555fa4fdeac20f1feac9fbf8be0f9315b16947b949ad138dd0
View on Chainz β†—

Height

#784,277

Difficulty

10.975123

Transactions

1

Size

207 B

Version

2

Bits

0af9a1a2

Nonce

2,086,526,537

Timestamp

10/26/2014, 6:46:56 PM

Confirmations

6,016,576

Merkle Root

f103849e666650deefa7746b577361a1971d87f5aca4ea95d261a8c049474c1b
Transactions (1)
Coinbasef103849e666650…61a8c049474c1b
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.688 Γ— 10⁹⁢(97-digit number)
16886174311956604157…10506299737297035360
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
1.688 Γ— 10⁹⁢(97-digit number)
16886174311956604157…10506299737297035359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.377 Γ— 10⁹⁢(97-digit number)
33772348623913208315…21012599474594070719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.754 Γ— 10⁹⁢(97-digit number)
67544697247826416630…42025198949188141439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.350 Γ— 10⁹⁷(98-digit number)
13508939449565283326…84050397898376282879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.701 Γ— 10⁹⁷(98-digit number)
27017878899130566652…68100795796752565759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.403 Γ— 10⁹⁷(98-digit number)
54035757798261133304…36201591593505131519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁸(99-digit number)
10807151559652226660…72403183187010263039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.161 Γ— 10⁹⁸(99-digit number)
21614303119304453321…44806366374020526079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.322 Γ— 10⁹⁸(99-digit number)
43228606238608906643…89612732748041052159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.645 Γ— 10⁹⁸(99-digit number)
86457212477217813286…79225465496082104319
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 784277

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 ab81f489dfbd8d555fa4fdeac20f1feac9fbf8be0f9315b16947b949ad138dd0

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 #784,277 on Chainz β†—
Circulating Supply:57,650,884 XPMΒ·at block #6,800,852 Β· updates every 60s
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