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Block #445,065

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/15/2014, 3:50:26 PM Β· Difficulty 10.3533 Β· 6,382,087 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee5ff399ad20490a1fa9687ecbdf121bd449dffc2368c07e4be0696a8544e76a
View on Chainz β†—

Height

#445,065

Difficulty

10.353293

Transactions

3

Size

618 B

Version

2

Bits

0a5a716c

Nonce

11,020,858

Timestamp

3/15/2014, 3:50:26 PM

Confirmations

6,382,087

Merkle Root

6106c15d1acf54833813a8252d247dfc7de6f572256683680381d9116faa6c6c
Transactions (3)
Coinbasee8b0d614dab3ac…e1d715f9a655d2
1 in β†’ 1 out9.3300 XPM109 B
AUWWiEg4…13AH7Vj6
4f5e903dfa57c8…726ad6fd6bd131
1 in β†’ 1 out56.2770 XPM193 B
ALg5VF6q…qkxSb5XC
1defab270dac38…c86ecbc9f1ac62
1 in β†’ 2 out9.2700 XPM226 B
AeuTc8Zy…cV2ArEY4AWKnGS1p…noKYDQrJ
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.

2.524 Γ— 10⁹⁡(96-digit number)
25240239416743597700…21264649596970231040
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
2.524 Γ— 10⁹⁡(96-digit number)
25240239416743597700…21264649596970231039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.048 Γ— 10⁹⁡(96-digit number)
50480478833487195400…42529299193940462079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.009 Γ— 10⁹⁢(97-digit number)
10096095766697439080…85058598387880924159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.019 Γ— 10⁹⁢(97-digit number)
20192191533394878160…70117196775761848319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.038 Γ— 10⁹⁢(97-digit number)
40384383066789756320…40234393551523696639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.076 Γ— 10⁹⁢(97-digit number)
80768766133579512640…80468787103047393279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.615 Γ— 10⁹⁷(98-digit number)
16153753226715902528…60937574206094786559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.230 Γ— 10⁹⁷(98-digit number)
32307506453431805056…21875148412189573119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.461 Γ— 10⁹⁷(98-digit number)
64615012906863610112…43750296824379146239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.292 Γ— 10⁹⁸(99-digit number)
12923002581372722022…87500593648758292479
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 445065

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 ee5ff399ad20490a1fa9687ecbdf121bd449dffc2368c07e4be0696a8544e76a

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 #445,065 on Chainz β†—
Circulating Supply:57,861,400 XPMΒ·at block #6,827,151 Β· updates every 60s
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