XPM Prime Explorer symbol
XPMPrime Explorer

Block #220,933

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/21/2013, 7:17:38 AM Β· Difficulty 9.9376 Β· 6,575,892 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
33aa498b51c245f77c9445229d7b1c09011bbb06a5c9a1251a48ee0267a50e07
View on Chainz β†—

Height

#220,933

Difficulty

9.937616

Transactions

1

Size

200 B

Version

2

Bits

09f00795

Nonce

42,690

Timestamp

10/21/2013, 7:17:38 AM

Confirmations

6,575,892

Mined by

⛏️ P2SHARjqnoYdpedZhatUCHm4eU4s4HFsP3c6ZD

Merkle Root

0cad180caba53dbf9f96ec5bf49b095402553bafe77f743061b8383b468be2da
Transactions (1)
Coinbase0cad180caba53d…b8383b468be2da
1 in β†’ 1 out10.1100 XPM109 B
ARjqnoYd…FsP3c6ZD
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.

5.553 Γ— 10⁹⁷(98-digit number)
55533039368264911809…61881808779637483519
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
5.553 Γ— 10⁹⁷(98-digit number)
55533039368264911809…61881808779637483519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁸(99-digit number)
11106607873652982361…23763617559274967039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.221 Γ— 10⁹⁸(99-digit number)
22213215747305964723…47527235118549934079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.442 Γ— 10⁹⁸(99-digit number)
44426431494611929447…95054470237099868159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.885 Γ— 10⁹⁸(99-digit number)
88852862989223858895…90108940474199736319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.777 Γ— 10⁹⁹(100-digit number)
17770572597844771779…80217880948399472639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.554 Γ— 10⁹⁹(100-digit number)
35541145195689543558…60435761896798945279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.108 Γ— 10⁹⁹(100-digit number)
71082290391379087116…20871523793597890559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.421 Γ— 10¹⁰⁰(101-digit number)
14216458078275817423…41743047587195781119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,618,610 XPMΒ·at block #6,796,824 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK