XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,075,337

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/18/2017, 2:11:04 AM Β· Difficulty 10.8412 Β· 4,769,504 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
26f788ff515c6222d48219d1e0162c8b333f80035f92c11c4ba6dc433e7c84ff
View on Chainz β†—

Height

#2,075,337

Difficulty

10.841165

Transactions

2

Size

981 B

Version

2

Bits

0ad7569e

Nonce

1,503,371,411

Timestamp

4/18/2017, 2:11:04 AM

Confirmations

4,769,504

Mined by

⛏️ P2SHAJzSeUodpTNZzLo3rPbb7Bg1aD1NhzBTZP

Merkle Root

19f7dd87fb8bcbaf3b32ec50c87b366d2ab81e0b3544f4fab06c4e1f6e723eca
Transactions (2)
Coinbasef1c626273c82f2…16782179d7bb45
1 in β†’ 1 out8.5000 XPM109 B
AJzSeUod…1NhzBTZP
90819d3fb1103a…5534eda3af99e5
5 in β†’ 1 out449.1400 XPM782 B
AMPKStip…imVv2KYN
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.

2.266 Γ— 10⁹⁡(96-digit number)
22664172155838739740…13787594404997117919
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
2.266 Γ— 10⁹⁡(96-digit number)
22664172155838739740…13787594404997117919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.532 Γ— 10⁹⁡(96-digit number)
45328344311677479480…27575188809994235839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.065 Γ— 10⁹⁡(96-digit number)
90656688623354958961…55150377619988471679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.813 Γ— 10⁹⁢(97-digit number)
18131337724670991792…10300755239976943359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.626 Γ— 10⁹⁢(97-digit number)
36262675449341983584…20601510479953886719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.252 Γ— 10⁹⁢(97-digit number)
72525350898683967169…41203020959907773439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.450 Γ— 10⁹⁷(98-digit number)
14505070179736793433…82406041919815546879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.901 Γ— 10⁹⁷(98-digit number)
29010140359473586867…64812083839631093759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.802 Γ— 10⁹⁷(98-digit number)
58020280718947173735…29624167679262187519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.160 Γ— 10⁹⁸(99-digit number)
11604056143789434747…59248335358524375039
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:58,003,137 XPMΒ·at block #6,844,840 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