XPM Prime Explorer symbol
XPMPrime Explorer

Block #857,020

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/17/2014, 1:00:36 PM Β· Difficulty 10.9676 Β· 5,986,152 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f85956b44c3aeca2f93eb9d015bcbd8cc0639ad1390d5c900da1898bb5cac7ba
View on Chainz β†—

Height

#857,020

Difficulty

10.967634

Transactions

2

Size

433 B

Version

2

Bits

0af7b6e1

Nonce

2,900,920,276

Timestamp

12/17/2014, 1:00:36 PM

Confirmations

5,986,152

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2ba8f4ef94d499fe4509dc8c4f51511f6ec2756296e2bc3d283d7473d660c593
Transactions (2)
Coinbase22ebed73f04776…2e0a72d2468092
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
de01af17cb5dc3…ba238d5e706636
1 in β†’ 2 out0.1478 XPM226 B
AGHdsmn7…4nw8HxPMARgk9vmd…QFGYpyok
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.

1.326 Γ— 10⁹⁢(97-digit number)
13261238437409303732…09072815203579402239
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
1.326 Γ— 10⁹⁢(97-digit number)
13261238437409303732…09072815203579402239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.652 Γ— 10⁹⁢(97-digit number)
26522476874818607465…18145630407158804479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.304 Γ— 10⁹⁢(97-digit number)
53044953749637214931…36291260814317608959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.060 Γ— 10⁹⁷(98-digit number)
10608990749927442986…72582521628635217919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.121 Γ— 10⁹⁷(98-digit number)
21217981499854885972…45165043257270435839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.243 Γ— 10⁹⁷(98-digit number)
42435962999709771945…90330086514540871679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.487 Γ— 10⁹⁷(98-digit number)
84871925999419543890…80660173029081743359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.697 Γ— 10⁹⁸(99-digit number)
16974385199883908778…61320346058163486719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.394 Γ— 10⁹⁸(99-digit number)
33948770399767817556…22640692116326973439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.789 Γ— 10⁹⁸(99-digit number)
67897540799535635112…45281384232653946879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.357 Γ— 10⁹⁹(100-digit number)
13579508159907127022…90562768465307893759
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:57,989,742 XPMΒ·at block #6,843,171 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