XPM Prime Explorer symbol
XPMPrime Explorer

Block #56,037

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2013, 5:25:37 AM Β· Difficulty 8.9461 Β· 6,751,143 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1a8962efc24d791c3b6f4009688300a50179d93cc2819659701902a53fe4cae4
View on Chainz β†—

Height

#56,037

Difficulty

8.946072

Transactions

1

Size

200 B

Version

2

Bits

08f231c0

Nonce

160

Timestamp

7/17/2013, 5:25:37 AM

Confirmations

6,751,143

Mined by

⛏️ P2SHAW9WWG6QijE5coo5J8R1E9HCsAznay3MF1

Merkle Root

d7f0407f43f004f4f8caf44cbf825f12c0caee95d4ad49ca20f4f161fe71e5bf
Transactions (1)
Coinbased7f0407f43f004…f4f161fe71e5bf
1 in β†’ 1 out12.4800 XPM110 B
AW9WWG6Q…znay3MF1
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.

2.309 Γ— 10⁹⁡(96-digit number)
23095516353427752590…75256741065238529111
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
2.309 Γ— 10⁹⁡(96-digit number)
23095516353427752590…75256741065238529111
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.619 Γ— 10⁹⁡(96-digit number)
46191032706855505181…50513482130477058221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.238 Γ— 10⁹⁡(96-digit number)
92382065413711010363…01026964260954116441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.847 Γ— 10⁹⁢(97-digit number)
18476413082742202072…02053928521908232881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.695 Γ— 10⁹⁢(97-digit number)
36952826165484404145…04107857043816465761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.390 Γ— 10⁹⁢(97-digit number)
73905652330968808290…08215714087632931521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.478 Γ— 10⁹⁷(98-digit number)
14781130466193761658…16431428175265863041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.956 Γ— 10⁹⁷(98-digit number)
29562260932387523316…32862856350531726081
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:57,701,451 XPMΒ·at block #6,807,179 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