XPM Prime Explorer symbol
XPMPrime Explorer

Block #249,302

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/7/2013, 9:21:18 PM Β· Difficulty 9.9667 Β· 6,553,860 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a84e56e55ee1057a233e5877d2ff8fbadd30782fd51427cd34cfde61e3a98c9f
View on Chainz β†—

Height

#249,302

Difficulty

9.966736

Transactions

2

Size

388 B

Version

2

Bits

09f77c09

Nonce

264,765

Timestamp

11/7/2013, 9:21:18 PM

Confirmations

6,553,860

Mined by

⛏️ P2SHAJHFE3qRqHgLWGFmv9ivAEt2du9XmuxJGM

Merkle Root

0a7e6e7a273d7612b4f2f1aac03aced41a9661e5c3fa289a4870346b7d22d213
Transactions (2)
Coinbasee009992fb9ed47…03376f42f7c269
1 in β†’ 1 out10.0600 XPM109 B
AJHFE3qR…9XmuxJGM
72e4bc7524bc73…d47be8fd49e6ea
1 in β†’ 1 out88.0071 XPM191 B
APH3Qiac…89d34WiU
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.

4.240 Γ— 10⁹⁰(91-digit number)
42400335217328042517…68574981785411100161
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
4.240 Γ— 10⁹⁰(91-digit number)
42400335217328042517…68574981785411100161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.480 Γ— 10⁹⁰(91-digit number)
84800670434656085035…37149963570822200321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.696 Γ— 10⁹¹(92-digit number)
16960134086931217007…74299927141644400641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.392 Γ— 10⁹¹(92-digit number)
33920268173862434014…48599854283288801281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.784 Γ— 10⁹¹(92-digit number)
67840536347724868028…97199708566577602561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.356 Γ— 10⁹²(93-digit number)
13568107269544973605…94399417133155205121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.713 Γ— 10⁹²(93-digit number)
27136214539089947211…88798834266310410241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.427 Γ— 10⁹²(93-digit number)
54272429078179894422…77597668532620820481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.085 Γ— 10⁹³(94-digit number)
10854485815635978884…55195337065241640961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.170 Γ— 10⁹³(94-digit number)
21708971631271957769…10390674130483281921
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:57,669,312 XPMΒ·at block #6,803,161 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