XPM Prime Explorer symbol
XPMPrime Explorer

Block #289,853

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2013, 9:54:47 AM Β· Difficulty 9.9888 Β· 6,513,204 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a09056cb0e1b2a4b325f0fa6bf1aed0a5e0ae699baa377dd9707092277e97816
View on Chainz β†—

Height

#289,853

Difficulty

9.988826

Transactions

1

Size

199 B

Version

2

Bits

09fd23ae

Nonce

32,202

Timestamp

12/2/2013, 9:54:47 AM

Confirmations

6,513,204

Mined by

⛏️ P2SHAYc3QGYaSv1sA3FuuZuBoiE4ttSWDuszQp

Merkle Root

490e6a9da61eb954e3f0cced6c614dff7a753651998c912e3117447162038cf0
Transactions (1)
Coinbase490e6a9da61eb9…17447162038cf0
1 in β†’ 1 out10.0100 XPM109 B
AYc3QGYa…SWDuszQp
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.

4.464 Γ— 10⁹⁡(96-digit number)
44648122999508879542…45888276720533071201
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
4.464 Γ— 10⁹⁡(96-digit number)
44648122999508879542…45888276720533071201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.929 Γ— 10⁹⁡(96-digit number)
89296245999017759085…91776553441066142401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.785 Γ— 10⁹⁢(97-digit number)
17859249199803551817…83553106882132284801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.571 Γ— 10⁹⁢(97-digit number)
35718498399607103634…67106213764264569601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.143 Γ— 10⁹⁢(97-digit number)
71436996799214207268…34212427528529139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.428 Γ— 10⁹⁷(98-digit number)
14287399359842841453…68424855057058278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.857 Γ— 10⁹⁷(98-digit number)
28574798719685682907…36849710114116556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.714 Γ— 10⁹⁷(98-digit number)
57149597439371365814…73699420228233113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.142 Γ— 10⁹⁸(99-digit number)
11429919487874273162…47398840456466227201
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:57,668,483 XPMΒ·at block #6,803,056 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