Block #462,903

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/27/2014, 5:59:50 PM · Difficulty 10.4165 · 6,342,297 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0dd16d8f505511f1b7ecc2b072d750feded785b027291fdf61572f0097a481ff

Height

#462,903

Difficulty

10.416531

Transactions

3

Size

803 B

Version

2

Bits

0a6aa1ce

Nonce

55,712

Timestamp

3/27/2014, 5:59:50 PM

Confirmations

6,342,297

Merkle Root

4a76901bf026185026af25a1559a0c955682077137ff7e4bf229c703159b5a13
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.

2.176 × 10¹⁰¹(102-digit number)
21763016030050819629…19536523462626141441
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
2.176 × 10¹⁰¹(102-digit number)
21763016030050819629…19536523462626141441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.352 × 10¹⁰¹(102-digit number)
43526032060101639259…39073046925252282881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.705 × 10¹⁰¹(102-digit number)
87052064120203278518…78146093850504565761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.741 × 10¹⁰²(103-digit number)
17410412824040655703…56292187701009131521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.482 × 10¹⁰²(103-digit number)
34820825648081311407…12584375402018263041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.964 × 10¹⁰²(103-digit number)
69641651296162622814…25168750804036526081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.392 × 10¹⁰³(104-digit number)
13928330259232524562…50337501608073052161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.785 × 10¹⁰³(104-digit number)
27856660518465049125…00675003216146104321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.571 × 10¹⁰³(104-digit number)
55713321036930098251…01350006432292208641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.114 × 10¹⁰⁴(105-digit number)
11142664207386019650…02700012864584417281
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:57,685,670 XPM·at block #6,805,199 · 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.