XPM Prime Explorer symbol
XPMPrime Explorer

Block #55,010

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 11:30:13 PM Β· Difficulty 8.9384 Β· 6,750,768 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ba3d65e3293383b286b42ab18673fc86006700f17ffc14879e6cf65db551ef41
View on Chainz β†—

Height

#55,010

Difficulty

8.938350

Transactions

1

Size

199 B

Version

2

Bits

08f037b8

Nonce

200

Timestamp

7/16/2013, 11:30:13 PM

Confirmations

6,750,768

Mined by

⛏️ P2SHAXY6feytV6ZxBQJFLAbLwdMRw9oghmWWGf

Merkle Root

48a830c932845ca4176dd0251836c55068dc66c3d2ded2898ce043a13a2485fb
Transactions (1)
Coinbase48a830c932845c…e043a13a2485fb
1 in β†’ 1 out12.5000 XPM110 B
AXY6feyt…oghmWWGf
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.

9.270 Γ— 10⁹²(93-digit number)
92704632560291902590…66003324958802347201
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
9.270 Γ— 10⁹²(93-digit number)
92704632560291902590…66003324958802347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.854 Γ— 10⁹³(94-digit number)
18540926512058380518…32006649917604694401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.708 Γ— 10⁹³(94-digit number)
37081853024116761036…64013299835209388801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.416 Γ— 10⁹³(94-digit number)
74163706048233522072…28026599670418777601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.483 Γ— 10⁹⁴(95-digit number)
14832741209646704414…56053199340837555201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.966 Γ— 10⁹⁴(95-digit number)
29665482419293408828…12106398681675110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.933 Γ— 10⁹⁴(95-digit number)
59330964838586817657…24212797363350220801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.186 Γ— 10⁹⁡(96-digit number)
11866192967717363531…48425594726700441601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,690,310 XPMΒ·at block #6,805,777 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