XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,681,643

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 11:43:05 AM Β· Difficulty 10.7165 Β· 5,162,498 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b8b47340fc811ce705f1f90600d720be125a776d8a47e11d380e3a0dd7672b5c
View on Chainz β†—

Height

#1,681,643

Difficulty

10.716455

Transactions

1

Size

201 B

Version

2

Bits

0ab7699e

Nonce

579,866,653

Timestamp

7/20/2016, 11:43:05 AM

Confirmations

5,162,498

Mined by

⛏️ P2SHAGBmz1S64JwxsRohuzvsrnnqZvcBwxQ3hc

Merkle Root

44ee5fda576917fc76875f7212b7a9df4617f0b95c9d3208b523edd7a64e9306
Transactions (1)
Coinbase44ee5fda576917…23edd7a64e9306
1 in β†’ 1 out8.6900 XPM110 B
AGBmz1S6…cBwxQ3hc
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.

1.506 Γ— 10⁹⁢(97-digit number)
15067144120600898107…71809314709990876161
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.506 Γ— 10⁹⁢(97-digit number)
15067144120600898107…71809314709990876161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.013 Γ— 10⁹⁢(97-digit number)
30134288241201796215…43618629419981752321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.026 Γ— 10⁹⁢(97-digit number)
60268576482403592431…87237258839963504641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.205 Γ— 10⁹⁷(98-digit number)
12053715296480718486…74474517679927009281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.410 Γ— 10⁹⁷(98-digit number)
24107430592961436972…48949035359854018561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.821 Γ— 10⁹⁷(98-digit number)
48214861185922873945…97898070719708037121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.642 Γ— 10⁹⁷(98-digit number)
96429722371845747890…95796141439416074241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.928 Γ— 10⁹⁸(99-digit number)
19285944474369149578…91592282878832148481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.857 Γ— 10⁹⁸(99-digit number)
38571888948738299156…83184565757664296961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.714 Γ— 10⁹⁸(99-digit number)
77143777897476598312…66369131515328593921
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,997,503 XPMΒ·at block #6,844,140 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