Block #892,401

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/12/2015, 1:46:26 PM · Difficulty 10.9522 · 5,907,084 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4228a5b8513939aa0ca86972ac676a272aae6deae4a8e2aca34a223891fc7b58

Height

#892,401

Difficulty

10.952222

Transactions

5

Size

3.82 KB

Version

2

Bits

0af3c4cd

Nonce

1,684,891,357

Timestamp

1/12/2015, 1:46:26 PM

Confirmations

5,907,084

Merkle Root

ac19834185785ae2bc0487bc445b81b0238cafd90471fb13632a7ad766ca4a32
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.

6.176 × 10⁹⁵(96-digit number)
61760572728520580782…84635544485629503039
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
6.176 × 10⁹⁵(96-digit number)
61760572728520580782…84635544485629503039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.235 × 10⁹⁶(97-digit number)
12352114545704116156…69271088971259006079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.470 × 10⁹⁶(97-digit number)
24704229091408232312…38542177942518012159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.940 × 10⁹⁶(97-digit number)
49408458182816464625…77084355885036024319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.881 × 10⁹⁶(97-digit number)
98816916365632929251…54168711770072048639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.976 × 10⁹⁷(98-digit number)
19763383273126585850…08337423540144097279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.952 × 10⁹⁷(98-digit number)
39526766546253171700…16674847080288194559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.905 × 10⁹⁷(98-digit number)
79053533092506343401…33349694160576389119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.581 × 10⁹⁸(99-digit number)
15810706618501268680…66699388321152778239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.162 × 10⁹⁸(99-digit number)
31621413237002537360…33398776642305556479
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,639,923 XPM·at block #6,799,484 · 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.