XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,050,602

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 3:35:27 AM Β· Difficulty 10.6967 Β· 4,759,353 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
082520822d250ca9a8a63f3f70cb8451842076b6c38c43bd847cc6edf824094f
View on Chainz β†—

Height

#2,050,602

Difficulty

10.696738

Transactions

2

Size

1.83 KB

Version

2

Bits

0ab25d6a

Nonce

127,794,204

Timestamp

4/3/2017, 3:35:27 AM

Confirmations

4,759,353

Mined by

⛏️ P2SHAM9q879q2ZAXkGgQRKF9dUosNKr1SeUgaH

Merkle Root

d66522fb3a841a705ddf3e9eb3074c7a84f23c3e1ae57ecbedd8aec0095390dd
Transactions (2)
Coinbaseb4c785e024e8f4…cd465eab487369
1 in β†’ 1 out8.7526 XPM109 B
AM9q879q…r1SeUgaH
4d834fac623405…9dd29fc1366ee5
11 in β†’ 1 out0.4600 XPM1.63 KB
AVPU2i57…kYsH8BA4
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.

1.343 Γ— 10⁹⁷(98-digit number)
13432190206854338049…39591187300486051839
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
1.343 Γ— 10⁹⁷(98-digit number)
13432190206854338049…39591187300486051839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.686 Γ— 10⁹⁷(98-digit number)
26864380413708676098…79182374600972103679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.372 Γ— 10⁹⁷(98-digit number)
53728760827417352197…58364749201944207359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁸(99-digit number)
10745752165483470439…16729498403888414719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁸(99-digit number)
21491504330966940878…33458996807776829439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.298 Γ— 10⁹⁸(99-digit number)
42983008661933881757…66917993615553658879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.596 Γ— 10⁹⁸(99-digit number)
85966017323867763515…33835987231107317759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁹(100-digit number)
17193203464773552703…67671974462214635519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.438 Γ— 10⁹⁹(100-digit number)
34386406929547105406…35343948924429271039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.877 Γ— 10⁹⁹(100-digit number)
68772813859094210812…70687897848858542079
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:57,723,721 XPMΒ·at block #6,809,954 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