XPM Prime Explorer symbol
XPMPrime Explorer

Block #851,998

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/13/2014, 5:56:37 PM Β· Difficulty 10.9702 Β· 5,989,574 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e693eb33a8dd4e3da3f356c265887ed09ac1bd6d3571263023452aeed625c4c9
View on Chainz β†—

Height

#851,998

Difficulty

10.970213

Transactions

2

Size

433 B

Version

2

Bits

0af85fe9

Nonce

725,990,103

Timestamp

12/13/2014, 5:56:37 PM

Confirmations

5,989,574

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

40b036e767e3518e4220dc2e115346d3c70863593a6bf10fdf0a329b139aa251
Transactions (2)
Coinbasef95c956ae7edb8…de4b1e6f86ac8f
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
d1fcc6ca4eb340…34cb57d1d55b0c
1 in β†’ 2 out0.0625 XPM226 B
Acpj55UP…K9scfej4AYUdHNQk…1KmSMg7V
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.

1.707 Γ— 10⁹⁷(98-digit number)
17074298092728747278…83541994220259864959
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
1.707 Γ— 10⁹⁷(98-digit number)
17074298092728747278…83541994220259864959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.414 Γ— 10⁹⁷(98-digit number)
34148596185457494557…67083988440519729919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.829 Γ— 10⁹⁷(98-digit number)
68297192370914989114…34167976881039459839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.365 Γ— 10⁹⁸(99-digit number)
13659438474182997822…68335953762078919679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.731 Γ— 10⁹⁸(99-digit number)
27318876948365995645…36671907524157839359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.463 Γ— 10⁹⁸(99-digit number)
54637753896731991291…73343815048315678719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.092 Γ— 10⁹⁹(100-digit number)
10927550779346398258…46687630096631357439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.185 Γ— 10⁹⁹(100-digit number)
21855101558692796516…93375260193262714879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.371 Γ— 10⁹⁹(100-digit number)
43710203117385593033…86750520386525429759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.742 Γ— 10⁹⁹(100-digit number)
87420406234771186066…73501040773050859519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.748 Γ— 10¹⁰⁰(101-digit number)
17484081246954237213…47002081546101719039
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:57,976,960 XPMΒ·at block #6,841,571 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