XPM Prime Explorer symbol
XPMPrime Explorer

Block #61,800

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 3:28:04 PM Β· Difficulty 8.9743 Β· 6,749,115 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c754439dd774ac3f7a7fe059e221a7871cffc8be5781f3d500d5ea513852c58d
View on Chainz β†—

Height

#61,800

Difficulty

8.974348

Transactions

1

Size

197 B

Version

2

Bits

08f96ede

Nonce

129

Timestamp

7/18/2013, 3:28:04 PM

Confirmations

6,749,115

Mined by

⛏️ P2SHAK1JUKWLjkgQU8N3MsSKyKCPeAoPR4rN5o

Merkle Root

64f28d217079680b0a4ba0b2e525ddc2e5b9b46462f46aca610a96a1fd31ba0c
Transactions (1)
Coinbase64f28d21707968…0a96a1fd31ba0c
1 in β†’ 1 out12.4000 XPM109 B
AK1JUKWL…oPR4rN5o
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.

1.517 Γ— 10⁹⁰(91-digit number)
15175027129176988218…71313509295556071629
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
1.517 Γ— 10⁹⁰(91-digit number)
15175027129176988218…71313509295556071629
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.035 Γ— 10⁹⁰(91-digit number)
30350054258353976436…42627018591112143259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.070 Γ— 10⁹⁰(91-digit number)
60700108516707952873…85254037182224286519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.214 Γ— 10⁹¹(92-digit number)
12140021703341590574…70508074364448573039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.428 Γ— 10⁹¹(92-digit number)
24280043406683181149…41016148728897146079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.856 Γ— 10⁹¹(92-digit number)
48560086813366362298…82032297457794292159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.712 Γ— 10⁹¹(92-digit number)
97120173626732724597…64064594915588584319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.942 Γ— 10⁹²(93-digit number)
19424034725346544919…28129189831177168639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.884 Γ— 10⁹²(93-digit number)
38848069450693089839…56258379662354337279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,731,421 XPMΒ·at block #6,810,914 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