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Block #172,259

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/20/2013, 2:54:32 AM Β· Difficulty 9.8626 Β· 6,640,533 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
37a33fcca6771791e9c63363a68ebe59eba849f8355f63ec423a731114bca7ee
View on Chainz β†—

Height

#172,259

Difficulty

9.862596

Transactions

2

Size

867 B

Version

2

Bits

09dcd315

Nonce

7,355

Timestamp

9/20/2013, 2:54:32 AM

Confirmations

6,640,533

Merkle Root

8160e3a8f88d28bcd49da5c615220886f94ffe5a2b835761677bd57e36d25361
Transactions (2)
Coinbase77c9edd9c88075…423c12e4535950
1 in β†’ 1 out10.2800 XPM109 B
AM1A9CZL…as4Lpogj
407e7a86757d16…533314c2f855ac
4 in β†’ 2 out2.0297 XPM669 B
AbDiu8Jt…CfHxzsoZAbjLQB3Y…SXLCXwVY
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.

1.346 Γ— 10⁹²(93-digit number)
13462886226714817166…50614300031491902380
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
1.346 Γ— 10⁹²(93-digit number)
13462886226714817166…50614300031491902379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.692 Γ— 10⁹²(93-digit number)
26925772453429634333…01228600062983804759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.385 Γ— 10⁹²(93-digit number)
53851544906859268667…02457200125967609519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.077 Γ— 10⁹³(94-digit number)
10770308981371853733…04914400251935219039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.154 Γ— 10⁹³(94-digit number)
21540617962743707466…09828800503870438079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.308 Γ— 10⁹³(94-digit number)
43081235925487414933…19657601007740876159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.616 Γ— 10⁹³(94-digit number)
86162471850974829867…39315202015481752319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.723 Γ— 10⁹⁴(95-digit number)
17232494370194965973…78630404030963504639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.446 Γ— 10⁹⁴(95-digit number)
34464988740389931947…57260808061927009279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.892 Γ— 10⁹⁴(95-digit number)
68929977480779863894…14521616123854018559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 172259

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 37a33fcca6771791e9c63363a68ebe59eba849f8355f63ec423a731114bca7ee

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 #172,259 on Chainz β†—
Circulating Supply:57,746,378 XPMΒ·at block #6,812,791 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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