XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,100,497

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/5/2017, 6:04:53 AM Β· Difficulty 10.8555 Β· 4,744,014 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a1252b4215a2fe208c6ddfb8493f4427567baf8ea919ae063270cb74ddb1dec5
View on Chainz β†—

Height

#2,100,497

Difficulty

10.855485

Transactions

1

Size

200 B

Version

2

Bits

0adb0110

Nonce

1,564,016,661

Timestamp

5/5/2017, 6:04:53 AM

Confirmations

4,744,014

Mined by

⛏️ P2SHAMuKeV6UqRnjPp45PNW6F2v1iq3F255cJ6

Merkle Root

c54769af953a7d9c4150025de0651e3fa41a6e5011f2ad54ed1ca21fb6c0d735
Transactions (1)
Coinbasec54769af953a7d…1ca21fb6c0d735
1 in β†’ 1 out8.4700 XPM110 B
AMuKeV6U…3F255cJ6
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.

5.612 Γ— 10⁹³(94-digit number)
56128109203707703847…24637061322019065599
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
5.612 Γ— 10⁹³(94-digit number)
56128109203707703847…24637061322019065599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.122 Γ— 10⁹⁴(95-digit number)
11225621840741540769…49274122644038131199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.245 Γ— 10⁹⁴(95-digit number)
22451243681483081539…98548245288076262399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.490 Γ— 10⁹⁴(95-digit number)
44902487362966163078…97096490576152524799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.980 Γ— 10⁹⁴(95-digit number)
89804974725932326156…94192981152305049599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.796 Γ— 10⁹⁡(96-digit number)
17960994945186465231…88385962304610099199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.592 Γ— 10⁹⁡(96-digit number)
35921989890372930462…76771924609220198399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.184 Γ— 10⁹⁡(96-digit number)
71843979780745860925…53543849218440396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁢(97-digit number)
14368795956149172185…07087698436880793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.873 Γ— 10⁹⁢(97-digit number)
28737591912298344370…14175396873761587199
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:58,000,485 XPMΒ·at block #6,844,510 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