XPM Prime Explorer symbol
XPMPrime Explorer

Block #166,856

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/16/2013, 4:48:48 AM Β· Difficulty 9.8687 Β· 6,632,043 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e46c3d8ff4bab75d00f15f9eec3d32711636b3fc274751a042461b36e363e99e
View on Chainz β†—

Height

#166,856

Difficulty

9.868679

Transactions

1

Size

200 B

Version

2

Bits

09de61b9

Nonce

1,885

Timestamp

9/16/2013, 4:48:48 AM

Confirmations

6,632,043

Mined by

⛏️ P2SHAK1PxfmQML85qBomVuaSRengfuqpq8MjPH

Merkle Root

f7cf8728465f36a9f05bcb2795ddf7040789fdfb5e6d715d27c84dcadd0aca2d
Transactions (1)
Coinbasef7cf8728465f36…c84dcadd0aca2d
1 in β†’ 1 out10.2500 XPM109 B
AK1PxfmQ…qpq8MjPH
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.

1.116 Γ— 10⁹⁷(98-digit number)
11167156629033736758…10722960768634595841
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
1.116 Γ— 10⁹⁷(98-digit number)
11167156629033736758…10722960768634595841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.233 Γ— 10⁹⁷(98-digit number)
22334313258067473516…21445921537269191681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.466 Γ— 10⁹⁷(98-digit number)
44668626516134947033…42891843074538383361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.933 Γ— 10⁹⁷(98-digit number)
89337253032269894067…85783686149076766721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.786 Γ— 10⁹⁸(99-digit number)
17867450606453978813…71567372298153533441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.573 Γ— 10⁹⁸(99-digit number)
35734901212907957627…43134744596307066881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.146 Γ— 10⁹⁸(99-digit number)
71469802425815915254…86269489192614133761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.429 Γ— 10⁹⁹(100-digit number)
14293960485163183050…72538978385228267521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.858 Γ— 10⁹⁹(100-digit number)
28587920970326366101…45077956770456535041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.717 Γ— 10⁹⁹(100-digit number)
57175841940652732203…90155913540913070081
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:57,635,233 XPMΒ·at block #6,798,898 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