Block #447,600

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/17/2014, 9:28:40 AM · Difficulty 10.3585 · 6,361,735 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7a0b0a8965cc5b6360ec24cd81ab2f0e0e25af68568da605cf820a1bb9cc008e

Height

#447,600

Difficulty

10.358531

Transactions

1

Size

970 B

Version

2

Bits

0a5bc8ae

Nonce

35,303

Timestamp

3/17/2014, 9:28:40 AM

Confirmations

6,361,735

Merkle Root

a442704ba68e64955fb955e4c360c3ab9087bef21553e39dbbde51a07331897c
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.

1.336 × 10⁹⁷(98-digit number)
13367690291298669752…99420251051815052799
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
1.336 × 10⁹⁷(98-digit number)
13367690291298669752…99420251051815052799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.673 × 10⁹⁷(98-digit number)
26735380582597339504…98840502103630105599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.347 × 10⁹⁷(98-digit number)
53470761165194679009…97681004207260211199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.069 × 10⁹⁸(99-digit number)
10694152233038935801…95362008414520422399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.138 × 10⁹⁸(99-digit number)
21388304466077871603…90724016829040844799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.277 × 10⁹⁸(99-digit number)
42776608932155743207…81448033658081689599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.555 × 10⁹⁸(99-digit number)
85553217864311486414…62896067316163379199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.711 × 10⁹⁹(100-digit number)
17110643572862297282…25792134632326758399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.422 × 10⁹⁹(100-digit number)
34221287145724594565…51584269264653516799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.844 × 10⁹⁹(100-digit number)
68442574291449189131…03168538529307033599
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:57,718,747 XPM·at block #6,809,334 · 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