XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,122,820

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2017, 9:29:43 PM Β· Difficulty 10.9156 Β· 4,721,066 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5240bbc37c8d64fd446ccba011fe1d0a0c6c3c14fdec5600a5ad09781f7c60d4
View on Chainz β†—

Height

#2,122,820

Difficulty

10.915641

Transactions

2

Size

722 B

Version

2

Bits

0aea6770

Nonce

756,786,113

Timestamp

5/18/2017, 9:29:43 PM

Confirmations

4,721,066

Mined by

⛏️ P2SHANq12jB9JKSFB9SsL5KtqUsFJmwn6Q2goB

Merkle Root

9d8ce1664f968ef34b7228580151d37b53ed7fb352ce91c3b0f71458683a2ad6
Transactions (2)
Coinbasef677ac9970f66b…8ba2db64d6416c
1 in β†’ 1 out8.3900 XPM109 B
ANq12jB9…wn6Q2goB
faae480aba06f4…f30aa627a68343
3 in β†’ 2 out2.0375 XPM523 B
AeYZTP6b…v53Q54vJAXFimkBM…fiLm8kYy
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.

4.115 Γ— 10⁹⁡(96-digit number)
41158432826771586655…76035103102382008961
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
4.115 Γ— 10⁹⁡(96-digit number)
41158432826771586655…76035103102382008961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.231 Γ— 10⁹⁡(96-digit number)
82316865653543173311…52070206204764017921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.646 Γ— 10⁹⁢(97-digit number)
16463373130708634662…04140412409528035841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.292 Γ— 10⁹⁢(97-digit number)
32926746261417269324…08280824819056071681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.585 Γ— 10⁹⁢(97-digit number)
65853492522834538649…16561649638112143361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.317 Γ— 10⁹⁷(98-digit number)
13170698504566907729…33123299276224286721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.634 Γ— 10⁹⁷(98-digit number)
26341397009133815459…66246598552448573441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.268 Γ— 10⁹⁷(98-digit number)
52682794018267630919…32493197104897146881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.053 Γ— 10⁹⁸(99-digit number)
10536558803653526183…64986394209794293761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.107 Γ— 10⁹⁸(99-digit number)
21073117607307052367…29972788419588587521
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:57,995,457 XPMΒ·at block #6,843,885 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