XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,064,546

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2015, 7:58:19 AM Β· Difficulty 10.7317 Β· 5,739,059 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b8198f0597c3848f10bbc4518cf53c0102afbb63761eb82439a4911755ab6bc6
View on Chainz β†—

Height

#1,064,546

Difficulty

10.731727

Transactions

2

Size

574 B

Version

2

Bits

0abb527a

Nonce

677,720,172

Timestamp

5/18/2015, 7:58:19 AM

Confirmations

5,739,059

Mined by

⛏️ P2SHAVkAAKhneAqhSr6Z5m9LwusjFjV5yPWHEn

Merkle Root

7caf6243a95eb49f24a4a1950c936dac2afb520a4d726dae2f28707a321bf9af
Transactions (2)
Coinbase17c7d2005b1696…79bed235304d0e
1 in β†’ 1 out8.6800 XPM109 B
AVkAAKhn…V5yPWHEn
a1269917d3f939…4826329ca08aff
2 in β†’ 2 out13.2444 XPM376 B
Ae9drWdk…FnLTm9PnAHhs1onU…6ZyL9CA1
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.

2.137 Γ— 10⁹³(94-digit number)
21372813860611235755…79004246586542092441
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
2.137 Γ— 10⁹³(94-digit number)
21372813860611235755…79004246586542092441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.274 Γ— 10⁹³(94-digit number)
42745627721222471510…58008493173084184881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.549 Γ— 10⁹³(94-digit number)
85491255442444943021…16016986346168369761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.709 Γ— 10⁹⁴(95-digit number)
17098251088488988604…32033972692336739521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.419 Γ— 10⁹⁴(95-digit number)
34196502176977977208…64067945384673479041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.839 Γ— 10⁹⁴(95-digit number)
68393004353955954416…28135890769346958081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.367 Γ— 10⁹⁡(96-digit number)
13678600870791190883…56271781538693916161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.735 Γ— 10⁹⁡(96-digit number)
27357201741582381766…12543563077387832321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.471 Γ— 10⁹⁡(96-digit number)
54714403483164763533…25087126154775664641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.094 Γ— 10⁹⁢(97-digit number)
10942880696632952706…50174252309551329281
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:57,672,879 XPMΒ·at block #6,803,604 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