Block #1,490,229

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/9/2016, 6:06:59 PM · Difficulty 10.6932 · 5,320,520 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a650b36d01f09206df643e69bef3d0da612f9220da5e8e8286c5dcf522790c01

Height

#1,490,229

Difficulty

10.693215

Transactions

2

Size

1.54 KB

Version

2

Bits

0ab17684

Nonce

1,379,839,520

Timestamp

3/9/2016, 6:06:59 PM

Confirmations

5,320,520

Merkle Root

84f515526a4012dd5cc681316258601185ae35235e3b252b73d60fe3224d970e
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.199 × 10⁹⁴(95-digit number)
71999759268995970019…88748703989791703041
Discovered Prime Numbers
p_k = 2^k × 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
7.199 × 10⁹⁴(95-digit number)
71999759268995970019…88748703989791703041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.439 × 10⁹⁵(96-digit number)
14399951853799194003…77497407979583406081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.879 × 10⁹⁵(96-digit number)
28799903707598388007…54994815959166812161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.759 × 10⁹⁵(96-digit number)
57599807415196776015…09989631918333624321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.151 × 10⁹⁶(97-digit number)
11519961483039355203…19979263836667248641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.303 × 10⁹⁶(97-digit number)
23039922966078710406…39958527673334497281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.607 × 10⁹⁶(97-digit number)
46079845932157420812…79917055346668994561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.215 × 10⁹⁶(97-digit number)
92159691864314841624…59834110693337989121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.843 × 10⁹⁷(98-digit number)
18431938372862968324…19668221386675978241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.686 × 10⁹⁷(98-digit number)
36863876745725936649…39336442773351956481
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,730,084 XPM·at block #6,810,748 · 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.

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.

·Privacy Policy