XPM Prime Explorer symbol
XPMPrime Explorer

Block #209,041

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2013, 8:54:06 AM Β· Difficulty 9.9081 Β· 6,607,006 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4812631f061c771548494ee86ca7eb2c9680a8d820fdcc3a98da86a423f7685d
View on Chainz β†—

Height

#209,041

Difficulty

9.908072

Transactions

1

Size

199 B

Version

2

Bits

09e87762

Nonce

218,207

Timestamp

10/14/2013, 8:54:06 AM

Confirmations

6,607,006

Mined by

⛏️ P2SHAMjEL5jU5FrR33MFDHGMbVsnwkXWAbZRhp

Merkle Root

0ef82467239693fc7e4c4e258a2d8c7fde5d0cfece3d10d1b29b7515f57ad258
Transactions (1)
Coinbase0ef82467239693…9b7515f57ad258
1 in β†’ 1 out10.1700 XPM109 B
AMjEL5jU…XWAbZRhp
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.

1.733 Γ— 10⁹⁡(96-digit number)
17331313417015088039…67887479819866725879
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
1.733 Γ— 10⁹⁡(96-digit number)
17331313417015088039…67887479819866725879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.466 Γ— 10⁹⁡(96-digit number)
34662626834030176078…35774959639733451759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.932 Γ— 10⁹⁡(96-digit number)
69325253668060352157…71549919279466903519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁢(97-digit number)
13865050733612070431…43099838558933807039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.773 Γ— 10⁹⁢(97-digit number)
27730101467224140863…86199677117867614079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.546 Γ— 10⁹⁢(97-digit number)
55460202934448281726…72399354235735228159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.109 Γ— 10⁹⁷(98-digit number)
11092040586889656345…44798708471470456319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.218 Γ— 10⁹⁷(98-digit number)
22184081173779312690…89597416942940912639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.436 Γ— 10⁹⁷(98-digit number)
44368162347558625380…79194833885881825279
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:57,772,492 XPMΒ·at block #6,816,046 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.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy