Block #922,302

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 9:02:10 AM · Difficulty 10.9158 · 5,876,543 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
38e279c09754a2fe9b179ebed38cd14260d89a064c698c884d76536dd4e3ef18

Height

#922,302

Difficulty

10.915755

Transactions

5

Size

115.98 KB

Version

2

Bits

0aea6eeb

Nonce

239,190,811

Timestamp

2/4/2015, 9:02:10 AM

Confirmations

5,876,543

Merkle Root

111df76494c39b879b494a21509d985c4cbfde6f460f364d7dc5eb56d29a25af
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1178.1261 XPM28.95 KB
200 in → 1 out1054.8257 XPM28.94 KB
200 in → 1 out1041.8918 XPM28.94 KB
200 in → 1 out893.8969 XPM28.95 KB
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.

1.852 × 10⁹⁶(97-digit number)
18521576069981058551…78317243401102555919
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
1.852 × 10⁹⁶(97-digit number)
18521576069981058551…78317243401102555919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.704 × 10⁹⁶(97-digit number)
37043152139962117103…56634486802205111839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.408 × 10⁹⁶(97-digit number)
74086304279924234206…13268973604410223679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.481 × 10⁹⁷(98-digit number)
14817260855984846841…26537947208820447359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.963 × 10⁹⁷(98-digit number)
29634521711969693682…53075894417640894719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.926 × 10⁹⁷(98-digit number)
59269043423939387365…06151788835281789439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.185 × 10⁹⁸(99-digit number)
11853808684787877473…12303577670563578879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.370 × 10⁹⁸(99-digit number)
23707617369575754946…24607155341127157759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.741 × 10⁹⁸(99-digit number)
47415234739151509892…49214310682254315519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.483 × 10⁹⁸(99-digit number)
94830469478303019784…98428621364508631039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.896 × 10⁹⁹(100-digit number)
18966093895660603956…96857242729017262079
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,634,793 XPM·at block #6,798,844 · 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.