Block #2,633,923

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/28/2018, 4:20:51 PM · Difficulty 11.2153 · 4,206,620 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1bf07d574b80c9cf98a62f3529bc4a064fbfbcbcd9f7b582f131b1dc3686968a

Height

#2,633,923

Difficulty

11.215262

Transactions

49

Size

16.38 KB

Version

2

Bits

0b371b70

Nonce

1,244,719,628

Timestamp

4/28/2018, 4:20:51 PM

Confirmations

4,206,620

Merkle Root

2f0ac31f7052b265ff9ca028060e9f3ee1d4bdc70b04cd508c3698154d717f06
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.

1.097 × 10⁹⁴(95-digit number)
10976730663902466675…94873356145971452839
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
1.097 × 10⁹⁴(95-digit number)
10976730663902466675…94873356145971452839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.195 × 10⁹⁴(95-digit number)
21953461327804933350…89746712291942905679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.390 × 10⁹⁴(95-digit number)
43906922655609866700…79493424583885811359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.781 × 10⁹⁴(95-digit number)
87813845311219733401…58986849167771622719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.756 × 10⁹⁵(96-digit number)
17562769062243946680…17973698335543245439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.512 × 10⁹⁵(96-digit number)
35125538124487893360…35947396671086490879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.025 × 10⁹⁵(96-digit number)
70251076248975786721…71894793342172981759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.405 × 10⁹⁶(97-digit number)
14050215249795157344…43789586684345963519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.810 × 10⁹⁶(97-digit number)
28100430499590314688…87579173368691927039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.620 × 10⁹⁶(97-digit number)
56200860999180629376…75158346737383854079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.124 × 10⁹⁷(98-digit number)
11240172199836125875…50316693474767708159
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:57,968,676 XPM·at block #6,840,542 · updates every 60s
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