XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,051,410

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 12:29:08 PM Β· Difficulty 10.7133 Β· 4,790,687 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
02e5653a6a29eb0e990f7b66740847fd70ae75997ec4092752d2d66957c57bca
View on Chainz β†—

Height

#2,051,410

Difficulty

10.713256

Transactions

1

Size

199 B

Version

2

Bits

0ab697f5

Nonce

1,049,507,852

Timestamp

4/3/2017, 12:29:08 PM

Confirmations

4,790,687

Mined by

⛏️ P2SHALsPmHGi5QEEEjMbpgTG5vBNxfaxigzuGb

Merkle Root

9df492ea4fe3e40806b4f4445caf9020fc8778e499c1f8bafbb7b9fa13453f24
Transactions (1)
Coinbase9df492ea4fe3e4…b7b9fa13453f24
1 in β†’ 1 out8.7000 XPM109 B
ALsPmHGi…axigzuGb
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.

4.150 Γ— 10⁹⁡(96-digit number)
41504858130363694983…32867199136605343039
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
4.150 Γ— 10⁹⁡(96-digit number)
41504858130363694983…32867199136605343039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.300 Γ— 10⁹⁡(96-digit number)
83009716260727389967…65734398273210686079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.660 Γ— 10⁹⁢(97-digit number)
16601943252145477993…31468796546421372159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.320 Γ— 10⁹⁢(97-digit number)
33203886504290955987…62937593092842744319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.640 Γ— 10⁹⁢(97-digit number)
66407773008581911974…25875186185685488639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.328 Γ— 10⁹⁷(98-digit number)
13281554601716382394…51750372371370977279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.656 Γ— 10⁹⁷(98-digit number)
26563109203432764789…03500744742741954559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.312 Γ— 10⁹⁷(98-digit number)
53126218406865529579…07001489485483909119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁸(99-digit number)
10625243681373105915…14002978970967818239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.125 Γ— 10⁹⁸(99-digit number)
21250487362746211831…28005957941935636479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.250 Γ— 10⁹⁸(99-digit number)
42500974725492423663…56011915883871272959
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:57,981,162 XPMΒ·at block #6,842,096 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