Block #492,055

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/14/2014, 9:16:31 PM · Difficulty 10.6874 · 6,301,525 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
134ebe135bb68ec816342b69b4b028123516f69164a4e268bcd87a0a6c6e60d2

Height

#492,055

Difficulty

10.687442

Transactions

1

Size

900 B

Version

2

Bits

0aaffc37

Nonce

66,844

Timestamp

4/14/2014, 9:16:31 PM

Confirmations

6,301,525

Merkle Root

efab320315d2c513fb0f5ac9225df38e7c8f1e71734523d05859cfe64f2b9bdf
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.

3.004 × 10⁹³(94-digit number)
30044031119462129710…83570016899421286771
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
3.004 × 10⁹³(94-digit number)
30044031119462129710…83570016899421286771
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.008 × 10⁹³(94-digit number)
60088062238924259420…67140033798842573541
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.201 × 10⁹⁴(95-digit number)
12017612447784851884…34280067597685147081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.403 × 10⁹⁴(95-digit number)
24035224895569703768…68560135195370294161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.807 × 10⁹⁴(95-digit number)
48070449791139407536…37120270390740588321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.614 × 10⁹⁴(95-digit number)
96140899582278815073…74240540781481176641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.922 × 10⁹⁵(96-digit number)
19228179916455763014…48481081562962353281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.845 × 10⁹⁵(96-digit number)
38456359832911526029…96962163125924706561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.691 × 10⁹⁵(96-digit number)
76912719665823052058…93924326251849413121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.538 × 10⁹⁶(97-digit number)
15382543933164610411…87848652503698826241
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:57,592,635 XPM·at block #6,793,579 · 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.