XPM Prime Explorer symbol
XPMPrime Explorer

Block #86,936

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2013, 12:20:17 PM Β· Difficulty 9.2842 Β· 6,709,886 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dec47ba89c3f40c6373cccc7d9fe0b4fa43522fe571319f9427a94a8fd40e230
View on Chainz β†—

Height

#86,936

Difficulty

9.284162

Transactions

1

Size

204 B

Version

2

Bits

0948bedf

Nonce

163,156

Timestamp

7/28/2013, 12:20:17 PM

Confirmations

6,709,886

Mined by

⛏️ P2SHAcuJraLTi7SA51dYsYdywtXJwqY66BS47Q

Merkle Root

06dd1dbb805b2061d32759e06356be204b9ef9a48f372395e67bcfbdb21e1052
Transactions (1)
Coinbase06dd1dbb805b20…7bcfbdb21e1052
1 in β†’ 1 out11.5800 XPM109 B
AcuJraLT…Y66BS47Q
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.

2.495 Γ— 10¹⁰⁡(106-digit number)
24950069448297173280…92758096342951828361
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
2.495 Γ— 10¹⁰⁡(106-digit number)
24950069448297173280…92758096342951828361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.990 Γ— 10¹⁰⁡(106-digit number)
49900138896594346560…85516192685903656721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.980 Γ— 10¹⁰⁡(106-digit number)
99800277793188693121…71032385371807313441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.996 Γ— 10¹⁰⁢(107-digit number)
19960055558637738624…42064770743614626881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.992 Γ— 10¹⁰⁢(107-digit number)
39920111117275477248…84129541487229253761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.984 Γ— 10¹⁰⁢(107-digit number)
79840222234550954497…68259082974458507521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.596 Γ— 10¹⁰⁷(108-digit number)
15968044446910190899…36518165948917015041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.193 Γ— 10¹⁰⁷(108-digit number)
31936088893820381798…73036331897834030081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.387 Γ— 10¹⁰⁷(108-digit number)
63872177787640763597…46072663795668060161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.277 Γ— 10¹⁰⁸(109-digit number)
12774435557528152719…92145327591336120321
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:57,618,585 XPMΒ·at block #6,796,821 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