XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,638,989

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 12:01:10 PM Β· Difficulty 11.5170 Β· 4,204,198 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
66bcf652e5cb86be074e21233e9ca83346e9103d337a1d3b6e8c5fcde003e46d
View on Chainz β†—

Height

#2,638,989

Difficulty

11.517012

Transactions

1

Size

200 B

Version

2

Bits

0b845ae7

Nonce

623,722,475

Timestamp

4/30/2018, 12:01:10 PM

Confirmations

4,204,198

Mined by

⛏️ P2SHAHWMmNg1uv4vuQHjnPDNudi5Cu8HF5x4dv

Merkle Root

6680b9844c25b5be9c0ddafc67a1df9c2492d85f0581fff2ea015378ea4d5088
Transactions (1)
Coinbase6680b9844c25b5…015378ea4d5088
1 in β†’ 1 out7.5300 XPM110 B
AHWMmNg1…8HF5x4dv
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.

6.409 Γ— 10⁹⁴(95-digit number)
64098797033120359922…70515061066471681839
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
6.409 Γ— 10⁹⁴(95-digit number)
64098797033120359922…70515061066471681839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.281 Γ— 10⁹⁡(96-digit number)
12819759406624071984…41030122132943363679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.563 Γ— 10⁹⁡(96-digit number)
25639518813248143969…82060244265886727359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.127 Γ— 10⁹⁡(96-digit number)
51279037626496287938…64120488531773454719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.025 Γ— 10⁹⁢(97-digit number)
10255807525299257587…28240977063546909439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.051 Γ— 10⁹⁢(97-digit number)
20511615050598515175…56481954127093818879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.102 Γ— 10⁹⁢(97-digit number)
41023230101197030350…12963908254187637759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.204 Γ— 10⁹⁢(97-digit number)
82046460202394060701…25927816508375275519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.640 Γ— 10⁹⁷(98-digit number)
16409292040478812140…51855633016750551039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.281 Γ— 10⁹⁷(98-digit number)
32818584080957624280…03711266033501102079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.563 Γ— 10⁹⁷(98-digit number)
65637168161915248560…07422532067002204159
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:57,989,864 XPMΒ·at block #6,843,186 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