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Block #673,901

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/11/2014, 9:25:45 PM Β· Difficulty 10.9653 Β· 6,141,188 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ff88637ba0eab3a8a6cdf2aea6869d51d57be4e304a287b460e2db8999c5b337
View on Chainz β†—

Height

#673,901

Difficulty

10.965333

Transactions

1

Size

207 B

Version

2

Bits

0af72012

Nonce

229,524,700

Timestamp

8/11/2014, 9:25:45 PM

Confirmations

6,141,188

Merkle Root

6a0a864276d34dcb6ed731faf9b7b0c97a6a4b1a88b36cfa38edfaa5278c0a28
Transactions (1)
Coinbase6a0a864276d34d…edfaa5278c0a28
1 in β†’ 1 out8.3000 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.

5.277 Γ— 10⁹⁢(97-digit number)
52771297266058533728…35814888153245409280
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
5.277 Γ— 10⁹⁢(97-digit number)
52771297266058533728…35814888153245409281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.055 Γ— 10⁹⁷(98-digit number)
10554259453211706745…71629776306490818561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.110 Γ— 10⁹⁷(98-digit number)
21108518906423413491…43259552612981637121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.221 Γ— 10⁹⁷(98-digit number)
42217037812846826982…86519105225963274241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.443 Γ— 10⁹⁷(98-digit number)
84434075625693653965…73038210451926548481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.688 Γ— 10⁹⁸(99-digit number)
16886815125138730793…46076420903853096961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.377 Γ— 10⁹⁸(99-digit number)
33773630250277461586…92152841807706193921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.754 Γ— 10⁹⁸(99-digit number)
67547260500554923172…84305683615412387841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.350 Γ— 10⁹⁹(100-digit number)
13509452100110984634…68611367230824775681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.701 Γ— 10⁹⁹(100-digit number)
27018904200221969268…37222734461649551361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.403 Γ— 10⁹⁹(100-digit number)
54037808400443938537…74445468923299102721
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 673901

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 ff88637ba0eab3a8a6cdf2aea6869d51d57be4e304a287b460e2db8999c5b337

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 #673,901 on Chainz β†—
Circulating Supply:57,764,800 XPMΒ·at block #6,815,088 Β· updates every 60s
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