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Block #680,078

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2014, 11:04:02 AM Β· Difficulty 10.9627 Β· 6,132,913 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fcc8cdd1187ea8366e301789f412c7f616d73d5b6696bf37d60159dbf06d6881
View on Chainz β†—

Height

#680,078

Difficulty

10.962690

Transactions

1

Size

206 B

Version

2

Bits

0af672de

Nonce

1,779,721,207

Timestamp

8/16/2014, 11:04:02 AM

Confirmations

6,132,913

Merkle Root

bbb840ce1c68fc1c958d389f9700eb3f709ee75ed69caac2680462394e4bde16
Transactions (1)
Coinbasebbb840ce1c68fc…0462394e4bde16
1 in β†’ 1 out8.3100 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.

3.552 Γ— 10⁹⁡(96-digit number)
35523783987796932662…47366288427724616000
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
3.552 Γ— 10⁹⁡(96-digit number)
35523783987796932662…47366288427724615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.104 Γ— 10⁹⁡(96-digit number)
71047567975593865324…94732576855449231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.420 Γ— 10⁹⁢(97-digit number)
14209513595118773064…89465153710898463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.841 Γ— 10⁹⁢(97-digit number)
28419027190237546129…78930307421796927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.683 Γ— 10⁹⁢(97-digit number)
56838054380475092259…57860614843593855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.136 Γ— 10⁹⁷(98-digit number)
11367610876095018451…15721229687187711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.273 Γ— 10⁹⁷(98-digit number)
22735221752190036903…31442459374375423999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.547 Γ— 10⁹⁷(98-digit number)
45470443504380073807…62884918748750847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.094 Γ— 10⁹⁷(98-digit number)
90940887008760147615…25769837497501695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.818 Γ— 10⁹⁸(99-digit number)
18188177401752029523…51539674995003391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.637 Γ— 10⁹⁸(99-digit number)
36376354803504059046…03079349990006783999
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 680078

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 fcc8cdd1187ea8366e301789f412c7f616d73d5b6696bf37d60159dbf06d6881

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 #680,078 on Chainz β†—
Circulating Supply:57,747,967 XPMΒ·at block #6,812,990 Β· updates every 60s
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