XPM Prime Explorer symbol
XPMPrime Explorer

Block #451,240

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/19/2014, 7:09:14 PM Β· Difficulty 10.3835 Β· 6,362,778 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
80e44380bf7149099383e707e6e366b412b8b988e1958a08837411f93f9ea382
View on Chainz β†—

Height

#451,240

Difficulty

10.383457

Transactions

1

Size

202 B

Version

2

Bits

0a622a35

Nonce

99,228

Timestamp

3/19/2014, 7:09:14 PM

Confirmations

6,362,778

Mined by

⛏️ P2SHASTRrh3oRuThcsrZSvcrRQUsVYuYdoYHdA

Merkle Root

379eac3b4171ac0e4e8fa917cbfbad64e9c0bc4a6e49e547aa48fe3790ee927e
Transactions (1)
Coinbase379eac3b4171ac…48fe3790ee927e
1 in β†’ 1 out9.2600 XPM111 B
ASTRrh3o…uYdoYHdA
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.

7.298 Γ— 10⁹⁢(97-digit number)
72988432349604086175…36717085221634867199
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
7.298 Γ— 10⁹⁢(97-digit number)
72988432349604086175…36717085221634867199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.459 Γ— 10⁹⁷(98-digit number)
14597686469920817235…73434170443269734399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.919 Γ— 10⁹⁷(98-digit number)
29195372939841634470…46868340886539468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.839 Γ— 10⁹⁷(98-digit number)
58390745879683268940…93736681773078937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.167 Γ— 10⁹⁸(99-digit number)
11678149175936653788…87473363546157875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.335 Γ— 10⁹⁸(99-digit number)
23356298351873307576…74946727092315750399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.671 Γ— 10⁹⁸(99-digit number)
46712596703746615152…49893454184631500799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.342 Γ— 10⁹⁸(99-digit number)
93425193407493230304…99786908369263001599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.868 Γ— 10⁹⁹(100-digit number)
18685038681498646060…99573816738526003199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.737 Γ— 10⁹⁹(100-digit number)
37370077362997292121…99147633477052006399
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:57,756,228 XPMΒ·at block #6,814,017 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