XPM Prime Explorer symbol
XPMPrime Explorer

Block #952,566

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/26/2015, 5:30:01 AM Β· Difficulty 10.8946 Β· 5,873,022 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
47e7565be9f08826f49ad11dccbdaad9d710fdb8d18cc741b1a24fdabff8cd4a
View on Chainz β†—

Height

#952,566

Difficulty

10.894567

Transactions

2

Size

4.03 KB

Version

2

Bits

0ae5025f

Nonce

30,128

Timestamp

2/26/2015, 5:30:01 AM

Confirmations

5,873,022

Mined by

⛏️ P2SHAT4me1AvZf8VyvR54NxSRAex8obz6JjojW

Merkle Root

91fcf2cd000ed2699f217bd34bf4a95e0e8c09bd3af07dd929328b1d534440d1
Transactions (2)
Coinbase6b5b917869864a…f1190371a32c1f
1 in β†’ 1 out8.4500 XPM109 B
AT4me1Av…bz6JjojW
fbbc6453f9828c…020ec95aa208c0
26 in β†’ 2 out100.8000 XPM3.84 KB
AYj1NzSe…ENdGNE2tAKF4UC7F…j9gwULfJ
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.

3.749 Γ— 10⁹⁡(96-digit number)
37493155081060989721…09180083763186810199
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
3.749 Γ— 10⁹⁡(96-digit number)
37493155081060989721…09180083763186810199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.498 Γ— 10⁹⁡(96-digit number)
74986310162121979442…18360167526373620399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.499 Γ— 10⁹⁢(97-digit number)
14997262032424395888…36720335052747240799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.999 Γ— 10⁹⁢(97-digit number)
29994524064848791777…73440670105494481599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.998 Γ— 10⁹⁢(97-digit number)
59989048129697583554…46881340210988963199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.199 Γ— 10⁹⁷(98-digit number)
11997809625939516710…93762680421977926399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.399 Γ— 10⁹⁷(98-digit number)
23995619251879033421…87525360843955852799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.799 Γ— 10⁹⁷(98-digit number)
47991238503758066843…75050721687911705599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.598 Γ— 10⁹⁷(98-digit number)
95982477007516133686…50101443375823411199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.919 Γ— 10⁹⁸(99-digit number)
19196495401503226737…00202886751646822399
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:57,848,804 XPMΒ·at block #6,825,587 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