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Block #689,464

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/23/2014, 5:22:39 PM Β· Difficulty 10.9542 Β· 6,109,762 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
59efdad052b2d7fca748c4c488a819bf302337817c1636b1bf21d917cf95f88b
View on Chainz β†—

Height

#689,464

Difficulty

10.954172

Transactions

3

Size

2.95 KB

Version

2

Bits

0af444a2

Nonce

609,777,870

Timestamp

8/23/2014, 5:22:39 PM

Confirmations

6,109,762

Merkle Root

3063c1a629728834961e340b67f764e4ef79bf5d6af2cc9e9ac6dfce98ce2018
Transactions (3)
Coinbaseade5e2af89886a…7591da39e6694a
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
09511464a5e075…366f5356f18502
17 in β†’ 2 out134.2240 XPM2.53 KB
APH8bmtW…2gwurZRtAWkdeMFz…8VqzqvKd
f88c9cd34b5b36…b3347c8849b3c7
1 in β†’ 2 out2.4928 XPM226 B
ARHn1ftP…zjFjQ9NwAJTsLJ89…rErdMt2e
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.

4.440 Γ— 10⁹⁡(96-digit number)
44408786410270682439…81505090949540831040
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
4.440 Γ— 10⁹⁡(96-digit number)
44408786410270682439…81505090949540831041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.881 Γ— 10⁹⁡(96-digit number)
88817572820541364878…63010181899081662081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.776 Γ— 10⁹⁢(97-digit number)
17763514564108272975…26020363798163324161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.552 Γ— 10⁹⁢(97-digit number)
35527029128216545951…52040727596326648321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.105 Γ— 10⁹⁢(97-digit number)
71054058256433091902…04081455192653296641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.421 Γ— 10⁹⁷(98-digit number)
14210811651286618380…08162910385306593281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.842 Γ— 10⁹⁷(98-digit number)
28421623302573236761…16325820770613186561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.684 Γ— 10⁹⁷(98-digit number)
56843246605146473522…32651641541226373121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.136 Γ— 10⁹⁸(99-digit number)
11368649321029294704…65303283082452746241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.273 Γ— 10⁹⁸(99-digit number)
22737298642058589408…30606566164905492481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.547 Γ— 10⁹⁸(99-digit number)
45474597284117178817…61213132329810984961
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 689464

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 59efdad052b2d7fca748c4c488a819bf302337817c1636b1bf21d917cf95f88b

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 #689,464 on Chainz β†—
Circulating Supply:57,637,850 XPMΒ·at block #6,799,225 Β· updates every 60s
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