Block #71,468

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 6:49:35 PM · Difficulty 8.9932 · 6,719,950 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d3f3bf2037987298a03be13b1f22b9c769bf351fede42003970b1000618907fd

Height

#71,468

Difficulty

8.993220

Transactions

1

Size

200 B

Version

2

Bits

08fe43a5

Nonce

93

Timestamp

7/20/2013, 6:49:35 PM

Confirmations

6,719,950

Merkle Root

b563db489988573521852538770ddafd73863d95c6dd33db624a9910e64ce216
Transactions (1)
1 in → 1 out12.3500 XPM110 B
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.

3.103 × 10⁹⁵(96-digit number)
31033116134903840554…93849427490331030391
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
3.103 × 10⁹⁵(96-digit number)
31033116134903840554…93849427490331030391
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.206 × 10⁹⁵(96-digit number)
62066232269807681108…87698854980662060781
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.241 × 10⁹⁶(97-digit number)
12413246453961536221…75397709961324121561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.482 × 10⁹⁶(97-digit number)
24826492907923072443…50795419922648243121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.965 × 10⁹⁶(97-digit number)
49652985815846144886…01590839845296486241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.930 × 10⁹⁶(97-digit number)
99305971631692289773…03181679690592972481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.986 × 10⁹⁷(98-digit number)
19861194326338457954…06363359381185944961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.972 × 10⁹⁷(98-digit number)
39722388652676915909…12726718762371889921
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,575,281 XPM·at block #6,791,417 · updates every 60s
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