XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,720,535

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2016, 11:45:53 PM Β· Difficulty 10.6750 Β· 5,088,083 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c629ca8e181b8a5bd7899dd617dbb5f2d3aebbf34e5f7e62a4b2393715493fda
View on Chainz β†—

Height

#1,720,535

Difficulty

10.675027

Transactions

1

Size

243 B

Version

2

Bits

0aacce93

Nonce

944,633,017

Timestamp

8/16/2016, 11:45:53 PM

Confirmations

5,088,083

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

076bafec4beb500b6a4e470c97242458b8a866b70995aa683b8e45691e8331e6
Transactions (1)
Coinbase076bafec4beb50…8e45691e8331e6
1 in β†’ 2 out8.7600 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

1.083 Γ— 10⁹⁷(98-digit number)
10834124584811877634…11712530959879577599
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
1.083 Γ— 10⁹⁷(98-digit number)
10834124584811877634…11712530959879577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.166 Γ— 10⁹⁷(98-digit number)
21668249169623755269…23425061919759155199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.333 Γ— 10⁹⁷(98-digit number)
43336498339247510539…46850123839518310399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.667 Γ— 10⁹⁷(98-digit number)
86672996678495021079…93700247679036620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.733 Γ— 10⁹⁸(99-digit number)
17334599335699004215…87400495358073241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.466 Γ— 10⁹⁸(99-digit number)
34669198671398008431…74800990716146483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.933 Γ— 10⁹⁸(99-digit number)
69338397342796016863…49601981432292966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁹(100-digit number)
13867679468559203372…99203962864585932799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.773 Γ— 10⁹⁹(100-digit number)
27735358937118406745…98407925729171865599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.547 Γ— 10⁹⁹(100-digit number)
55470717874236813490…96815851458343731199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,712,994 XPMΒ·at block #6,808,617 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