XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,685,585

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2018, 8:31:43 AM Β· Difficulty 11.6873 Β· 4,159,188 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f2609234e32d0043a46c6dd4d3a65598964bc6c310ea620b667b1c184df51b17
View on Chainz β†—

Height

#2,685,585

Difficulty

11.687345

Transactions

1

Size

199 B

Version

2

Bits

0baff5d0

Nonce

1,219,934,699

Timestamp

5/31/2018, 8:31:43 AM

Confirmations

4,159,188

Mined by

⛏️ P2SHAPpcaeL3TG97uspU7ACqhez4DEjyd4MqWp

Merkle Root

7e51c1e3930311b2a07c0402fee119c82c56232f3b5c8fc5b75a6de0829260f7
Transactions (1)
Coinbase7e51c1e3930311…5a6de0829260f7
1 in β†’ 1 out7.3100 XPM110 B
APpcaeL3…jyd4MqWp
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.

2.357 Γ— 10⁹³(94-digit number)
23576072951553518506…18998000985885942979
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
2.357 Γ— 10⁹³(94-digit number)
23576072951553518506…18998000985885942979
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.715 Γ— 10⁹³(94-digit number)
47152145903107037012…37996001971771885959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.430 Γ— 10⁹³(94-digit number)
94304291806214074024…75992003943543771919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.886 Γ— 10⁹⁴(95-digit number)
18860858361242814804…51984007887087543839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.772 Γ— 10⁹⁴(95-digit number)
37721716722485629609…03968015774175087679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.544 Γ— 10⁹⁴(95-digit number)
75443433444971259219…07936031548350175359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.508 Γ— 10⁹⁡(96-digit number)
15088686688994251843…15872063096700350719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.017 Γ— 10⁹⁡(96-digit number)
30177373377988503687…31744126193400701439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.035 Γ— 10⁹⁡(96-digit number)
60354746755977007375…63488252386801402879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.207 Γ— 10⁹⁢(97-digit number)
12070949351195401475…26976504773602805759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.414 Γ— 10⁹⁢(97-digit number)
24141898702390802950…53953009547205611519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,002,597 XPMΒ·at block #6,844,772 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