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Home/Chain Registry/Block #1,687,308

Block #1,687,308

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/24/2016, 12:05:08 PM Β· Difficulty 10.7101 Β· 5,138,335 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
452ec4e197b479e57e3f5c5c5acd02b967be48410d214a30d331bc1bb6a0538c
View on Chainz β†—

Difficulty

10.710113

Transactions

1

Size

200 B

Version

2

Bits

0ab5c9f7

Nonce

902,619,419

Timestamp

7/24/2016, 12:05:08 PM

Confirmations

5,138,335

Merkle Root

8f4203b3718e1eb138ae5b62c892ab4f166118df748e2c5fc815ff9eee1c3fcc
Transactions (1)
Coinbase8f4203b3718e1e…15ff9eee1c3fcc
1 in β†’ 1 out8.7000 XPM109 B
ARLcU8os…EBEnTCL2
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.

4.075 Γ— 10⁹⁷(98-digit number)
40752386765653553559…70272426449780377600
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
4.075 Γ— 10⁹⁷(98-digit number)
40752386765653553559…70272426449780377599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.150 Γ— 10⁹⁷(98-digit number)
81504773531307107119…40544852899560755199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.630 Γ— 10⁹⁸(99-digit number)
16300954706261421423…81089705799121510399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.260 Γ— 10⁹⁸(99-digit number)
32601909412522842847…62179411598243020799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.520 Γ— 10⁹⁸(99-digit number)
65203818825045685695…24358823196486041599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.304 Γ— 10⁹⁹(100-digit number)
13040763765009137139…48717646392972083199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.608 Γ— 10⁹⁹(100-digit number)
26081527530018274278…97435292785944166399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.216 Γ— 10⁹⁹(100-digit number)
52163055060036548556…94870585571888332799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.043 Γ— 10¹⁰⁰(101-digit number)
10432611012007309711…89741171143776665599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.086 Γ— 10¹⁰⁰(101-digit number)
20865222024014619422…79482342287553331199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.173 Γ— 10¹⁰⁰(101-digit number)
41730444048029238845…58964684575106662399
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 1687308

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 452ec4e197b479e57e3f5c5c5acd02b967be48410d214a30d331bc1bb6a0538c

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 #1,687,308 on Chainz β†—
Circulating Supply:57,849,249 XPMΒ·at block #6,825,642 Β· updates every 60s
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