XPM Prime Explorer symbol
XPMPrime Explorer

Block #73,163

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 4:18:36 AM Β· Difficulty 8.9946 Β· 6,735,555 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
708fc1d1b40a858bda7dc595f6166d04273fefe6ede21cba2f7e3e6fcf8ed3a0
View on Chainz β†—

Height

#73,163

Difficulty

8.994623

Transactions

1

Size

199 B

Version

2

Bits

08fe9f9f

Nonce

65

Timestamp

7/21/2013, 4:18:36 AM

Confirmations

6,735,555

Mined by

⛏️ P2SHAPuKQSxsaJ7p3wx9uycmBYLihn5YJgufZx

Merkle Root

7b1ad7c9d68b8bbc51feda710332b7f8c88188c372d4e7b3ea59dca5716b66c9
Transactions (1)
Coinbase7b1ad7c9d68b8b…59dca5716b66c9
1 in β†’ 1 out12.3400 XPM109 B
APuKQSxs…5YJgufZx
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.

1.019 Γ— 10⁹⁡(96-digit number)
10199056455197050222…30109761642201781401
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
1.019 Γ— 10⁹⁡(96-digit number)
10199056455197050222…30109761642201781401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.039 Γ— 10⁹⁡(96-digit number)
20398112910394100444…60219523284403562801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.079 Γ— 10⁹⁡(96-digit number)
40796225820788200888…20439046568807125601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.159 Γ— 10⁹⁡(96-digit number)
81592451641576401777…40878093137614251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.631 Γ— 10⁹⁢(97-digit number)
16318490328315280355…81756186275228502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.263 Γ— 10⁹⁢(97-digit number)
32636980656630560710…63512372550457004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.527 Γ— 10⁹⁢(97-digit number)
65273961313261121421…27024745100914009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.305 Γ— 10⁹⁷(98-digit number)
13054792262652224284…54049490201828019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.610 Γ— 10⁹⁷(98-digit number)
26109584525304448568…08098980403656038401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,713,789 XPMΒ·at block #6,808,717 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

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