XPM Prime Explorer symbol
XPMPrime Explorer

Block #233,896

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/30/2013, 12:13:54 AM Β· Difficulty 9.9432 Β· 6,573,582 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2a855d4d9b8d6febde95926809460feb7de44e6dc6f1c56eb9df5aa41e0794b8
View on Chainz β†—

Height

#233,896

Difficulty

9.943176

Transactions

1

Size

199 B

Version

2

Bits

09f173fc

Nonce

354,295

Timestamp

10/30/2013, 12:13:54 AM

Confirmations

6,573,582

Mined by

⛏️ P2SHAFv4GxfhFidL8Dd2giAFtoCmE3LfEWFx48

Merkle Root

cc6b83f2f57467041d80d40a913ae802d8aa151516e17391c6b3d9b113f1f1d2
Transactions (1)
Coinbasecc6b83f2f57467…b3d9b113f1f1d2
1 in β†’ 1 out10.1000 XPM109 B
AFv4Gxfh…LfEWFx48
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.

1.392 Γ— 10⁹⁡(96-digit number)
13925878800481846406…37801871271862316319
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
1.392 Γ— 10⁹⁡(96-digit number)
13925878800481846406…37801871271862316319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.785 Γ— 10⁹⁡(96-digit number)
27851757600963692813…75603742543724632639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.570 Γ— 10⁹⁡(96-digit number)
55703515201927385626…51207485087449265279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.114 Γ— 10⁹⁢(97-digit number)
11140703040385477125…02414970174898530559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.228 Γ— 10⁹⁢(97-digit number)
22281406080770954250…04829940349797061119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.456 Γ— 10⁹⁢(97-digit number)
44562812161541908501…09659880699594122239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.912 Γ— 10⁹⁢(97-digit number)
89125624323083817002…19319761399188244479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.782 Γ— 10⁹⁷(98-digit number)
17825124864616763400…38639522798376488959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.565 Γ— 10⁹⁷(98-digit number)
35650249729233526801…77279045596752977919
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:57,703,850 XPMΒ·at block #6,807,477 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

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