Block #372,300

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/23/2014, 12:26:55 PM · Difficulty 10.4272 · 6,435,718 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b20ca2cbfdb9a99c8aed610d2e09bcc0292d075b0621d658fd66701141691633

Height

#372,300

Difficulty

10.427166

Transactions

1

Size

973 B

Version

2

Bits

0a6d5ac7

Nonce

24,797

Timestamp

1/23/2014, 12:26:55 PM

Confirmations

6,435,718

Merkle Root

acd5a133e81f1ebedad7d915c15bad4bcef4f087a9675e9f80469ce577216ce8
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.

6.503 × 10¹⁰³(104-digit number)
65036822772333691899…40743921726919943321
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
6.503 × 10¹⁰³(104-digit number)
65036822772333691899…40743921726919943321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.300 × 10¹⁰⁴(105-digit number)
13007364554466738379…81487843453839886641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.601 × 10¹⁰⁴(105-digit number)
26014729108933476759…62975686907679773281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.202 × 10¹⁰⁴(105-digit number)
52029458217866953519…25951373815359546561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.040 × 10¹⁰⁵(106-digit number)
10405891643573390703…51902747630719093121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.081 × 10¹⁰⁵(106-digit number)
20811783287146781407…03805495261438186241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.162 × 10¹⁰⁵(106-digit number)
41623566574293562815…07610990522876372481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.324 × 10¹⁰⁵(106-digit number)
83247133148587125631…15221981045752744961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.664 × 10¹⁰⁶(107-digit number)
16649426629717425126…30443962091505489921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.329 × 10¹⁰⁶(107-digit number)
33298853259434850252…60887924183010979841
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,708,186 XPM·at block #6,808,017 · 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