Block #3,008,396

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/13/2019, 9:46:37 PM · Difficulty 11.2035 · 3,834,694 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a551fac4bc494988297af9c7bb1f89ca51ec48c09e5797b18bd9fedd37cd2c0e

Height

#3,008,396

Difficulty

11.203540

Transactions

22

Size

5.57 KB

Version

2

Bits

0b341b36

Nonce

1,364,380,638

Timestamp

1/13/2019, 9:46:37 PM

Confirmations

3,834,694

Merkle Root

01517437f779dbd4bd0f69835e5a6972ebdaf52568e880278bcb9465cd75ae9d
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.

3.758 × 10⁹⁴(95-digit number)
37583300970590388217…15945931111805419519
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
3.758 × 10⁹⁴(95-digit number)
37583300970590388217…15945931111805419519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.516 × 10⁹⁴(95-digit number)
75166601941180776434…31891862223610839039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.503 × 10⁹⁵(96-digit number)
15033320388236155286…63783724447221678079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.006 × 10⁹⁵(96-digit number)
30066640776472310573…27567448894443356159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.013 × 10⁹⁵(96-digit number)
60133281552944621147…55134897788886712319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.202 × 10⁹⁶(97-digit number)
12026656310588924229…10269795577773424639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.405 × 10⁹⁶(97-digit number)
24053312621177848459…20539591155546849279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.810 × 10⁹⁶(97-digit number)
48106625242355696918…41079182311093698559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.621 × 10⁹⁶(97-digit number)
96213250484711393836…82158364622187397119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.924 × 10⁹⁷(98-digit number)
19242650096942278767…64316729244374794239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.848 × 10⁹⁷(98-digit number)
38485300193884557534…28633458488749588479
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:57,989,082 XPM·at block #6,843,089 · updates every 60s
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