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Block #680,110

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/16/2014, 11:43:21 AM Β· Difficulty 10.9627 Β· 6,132,409 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2604903072cbf51a8747db3e1f25e39adc2404d232bdf7df5f1c5a6f1cb4ce9e
View on Chainz β†—

Height

#680,110

Difficulty

10.962651

Transactions

1

Size

207 B

Version

2

Bits

0af67045

Nonce

216,227,501

Timestamp

8/16/2014, 11:43:21 AM

Confirmations

6,132,409

Merkle Root

7a52c3bb34558634b7e86af9e86ba0198dbd07daac0fea6c1a9dffa1ef244d9a
Transactions (1)
Coinbase7a52c3bb345586…9dffa1ef244d9a
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.

1.030 Γ— 10⁹⁷(98-digit number)
10307675872755720916…53529411477779952640
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.030 Γ— 10⁹⁷(98-digit number)
10307675872755720916…53529411477779952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.061 Γ— 10⁹⁷(98-digit number)
20615351745511441833…07058822955559905281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.123 Γ— 10⁹⁷(98-digit number)
41230703491022883666…14117645911119810561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.246 Γ— 10⁹⁷(98-digit number)
82461406982045767333…28235291822239621121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.649 Γ— 10⁹⁸(99-digit number)
16492281396409153466…56470583644479242241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.298 Γ— 10⁹⁸(99-digit number)
32984562792818306933…12941167288958484481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.596 Γ— 10⁹⁸(99-digit number)
65969125585636613867…25882334577916968961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.319 Γ— 10⁹⁹(100-digit number)
13193825117127322773…51764669155833937921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.638 Γ— 10⁹⁹(100-digit number)
26387650234254645546…03529338311667875841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.277 Γ— 10⁹⁹(100-digit number)
52775300468509291093…07058676623335751681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.055 Γ— 10¹⁰⁰(101-digit number)
10555060093701858218…14117353246671503361
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 680110

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 2604903072cbf51a8747db3e1f25e39adc2404d232bdf7df5f1c5a6f1cb4ce9e

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 #680,110 on Chainz β†—
Circulating Supply:57,744,186 XPMΒ·at block #6,812,518 Β· updates every 60s
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