XPM Prime Explorer symbol
XPMPrime Explorer

Block #901,488

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/19/2015, 2:30:34 PM Β· Difficulty 10.9416 Β· 5,908,141 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
187fdc2d6a3bde814cc4e980bfb8fd5e681af31ac44c0652ce8d7aab81c0aadf
View on Chainz β†—

Height

#901,488

Difficulty

10.941643

Transactions

2

Size

1.69 KB

Version

2

Bits

0af10f86

Nonce

219,778,830

Timestamp

1/19/2015, 2:30:34 PM

Confirmations

5,908,141

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2326114d7a96dd446ce33cf156434c4733833139606fd038e1a5db5399813881
Transactions (2)
Coinbase4bbeb0387a122b…5b4677b545c15a
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
3f01e44577e023…80fb30c709bcd9
10 in β†’ 1 out3991.9000 XPM1.49 KB
AGf4bxML…tCqWcVMH
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.

1.862 Γ— 10⁹⁡(96-digit number)
18625736866722738338…58264631760961364519
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
1.862 Γ— 10⁹⁡(96-digit number)
18625736866722738338…58264631760961364519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.725 Γ— 10⁹⁡(96-digit number)
37251473733445476677…16529263521922729039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.450 Γ— 10⁹⁡(96-digit number)
74502947466890953355…33058527043845458079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.490 Γ— 10⁹⁢(97-digit number)
14900589493378190671…66117054087690916159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.980 Γ— 10⁹⁢(97-digit number)
29801178986756381342…32234108175381832319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.960 Γ— 10⁹⁢(97-digit number)
59602357973512762684…64468216350763664639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.192 Γ— 10⁹⁷(98-digit number)
11920471594702552536…28936432701527329279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.384 Γ— 10⁹⁷(98-digit number)
23840943189405105073…57872865403054658559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.768 Γ— 10⁹⁷(98-digit number)
47681886378810210147…15745730806109317119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.536 Γ— 10⁹⁷(98-digit number)
95363772757620420295…31491461612218634239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.907 Γ— 10⁹⁸(99-digit number)
19072754551524084059…62982923224437268479
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:57,721,110 XPMΒ·at block #6,809,628 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