XPM Prime Explorer symbol
XPMPrime Explorer

Block #259,710

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/13/2013, 6:41:18 PM Β· Difficulty 9.9776 Β· 6,536,449 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
83589398b65374e5fcbdc7a7b9a432e4ca2705ffe9e9ef64627cd8e140de4b70
View on Chainz β†—

Height

#259,710

Difficulty

9.977594

Transactions

2

Size

425 B

Version

2

Bits

09fa4396

Nonce

119,299

Timestamp

11/13/2013, 6:41:18 PM

Confirmations

6,536,449

Mined by

⛏️ P2SHALXw9QTn863hGUhcKDQio8dCBVrmU5FCJu

Merkle Root

88ac365ef78b37d5b08c62cc67babe7fac6dbdbc545526277323aa31b7805192
Transactions (2)
Coinbase5529ff9e91d971…4068706a5f666b
1 in β†’ 1 out10.0400 XPM109 B
ALXw9QTn…rmU5FCJu
24465c1188c84d…86514888fc9d51
1 in β†’ 2 out95.9167 XPM226 B
ASfFwSSr…A3nK5Zb5AZdmkNt9…Dk8ffFeU
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.

5.264 Γ— 10⁹³(94-digit number)
52643506391931019101…25136366442791613441
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
5.264 Γ— 10⁹³(94-digit number)
52643506391931019101…25136366442791613441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.052 Γ— 10⁹⁴(95-digit number)
10528701278386203820…50272732885583226881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.105 Γ— 10⁹⁴(95-digit number)
21057402556772407640…00545465771166453761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.211 Γ— 10⁹⁴(95-digit number)
42114805113544815280…01090931542332907521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.422 Γ— 10⁹⁴(95-digit number)
84229610227089630561…02181863084665815041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.684 Γ— 10⁹⁡(96-digit number)
16845922045417926112…04363726169331630081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.369 Γ— 10⁹⁡(96-digit number)
33691844090835852224…08727452338663260161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.738 Γ— 10⁹⁡(96-digit number)
67383688181671704449…17454904677326520321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.347 Γ— 10⁹⁢(97-digit number)
13476737636334340889…34909809354653040641
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:57,613,268 XPMΒ·at block #6,796,158 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