XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,196,056

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/6/2017, 5:41:10 PM Β· Difficulty 10.9539 Β· 4,647,698 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a00eb4c6d852369fcf361e1497a44467f7e27b0b7248d6870bd02ceaec6882a5
View on Chainz β†—

Height

#2,196,056

Difficulty

10.953882

Transactions

2

Size

426 B

Version

2

Bits

0af431a2

Nonce

41,291,962

Timestamp

7/6/2017, 5:41:10 PM

Confirmations

4,647,698

Mined by

⛏️ P2SHAHLNpeUsnLBQFyqhUfE9p6mvrvr6D7V2eq

Merkle Root

eb8c8de6d2d32427da1d8e98b922c1fa9e64ec8d6878338e443da8bb561b9bcd
Transactions (2)
Coinbase5954e86759d166…1192a1f61718fd
1 in β†’ 1 out8.3300 XPM109 B
AHLNpeUs…r6D7V2eq
f9ef3041f77d89…f988ed64e2c02a
1 in β†’ 2 out10584.7141 XPM227 B
ARPxBo5Z…SwQXepmHAHJbFw5G…vhJuo6Uc
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.

1.239 Γ— 10⁹⁴(95-digit number)
12393967559407475394…50101314246689216499
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
1.239 Γ— 10⁹⁴(95-digit number)
12393967559407475394…50101314246689216499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.478 Γ— 10⁹⁴(95-digit number)
24787935118814950788…00202628493378432999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.957 Γ— 10⁹⁴(95-digit number)
49575870237629901577…00405256986756865999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.915 Γ— 10⁹⁴(95-digit number)
99151740475259803155…00810513973513731999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.983 Γ— 10⁹⁡(96-digit number)
19830348095051960631…01621027947027463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.966 Γ— 10⁹⁡(96-digit number)
39660696190103921262…03242055894054927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.932 Γ— 10⁹⁡(96-digit number)
79321392380207842524…06484111788109855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.586 Γ— 10⁹⁢(97-digit number)
15864278476041568504…12968223576219711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.172 Γ— 10⁹⁢(97-digit number)
31728556952083137009…25936447152439423999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.345 Γ— 10⁹⁢(97-digit number)
63457113904166274019…51872894304878847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.269 Γ— 10⁹⁷(98-digit number)
12691422780833254803…03745788609757695999
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:57,994,403 XPMΒ·at block #6,843,753 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