Block #160,147

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/11/2013, 5:07:33 PM · Difficulty 9.8618 · 6,631,404 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9bd60b0f1fa8ab98c38af21becc4e6113484861ba6b3fba88f8d9fc1711c50db

Height

#160,147

Difficulty

9.861825

Transactions

1

Size

199 B

Version

2

Bits

09dca090

Nonce

12,126

Timestamp

9/11/2013, 5:07:33 PM

Confirmations

6,631,404

Merkle Root

71e36e5a952912c0556f057f463907b68abb48d52b7e2fc13ef1182100ca67e0
Transactions (1)
1 in → 1 out10.2700 XPM109 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.

4.157 × 10⁹³(94-digit number)
41575176852064759671…33768162687590643201
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
4.157 × 10⁹³(94-digit number)
41575176852064759671…33768162687590643201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.315 × 10⁹³(94-digit number)
83150353704129519343…67536325375181286401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.663 × 10⁹⁴(95-digit number)
16630070740825903868…35072650750362572801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.326 × 10⁹⁴(95-digit number)
33260141481651807737…70145301500725145601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.652 × 10⁹⁴(95-digit number)
66520282963303615474…40290603001450291201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.330 × 10⁹⁵(96-digit number)
13304056592660723094…80581206002900582401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.660 × 10⁹⁵(96-digit number)
26608113185321446189…61162412005801164801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.321 × 10⁹⁵(96-digit number)
53216226370642892379…22324824011602329601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.064 × 10⁹⁶(97-digit number)
10643245274128578475…44649648023204659201
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,576,357 XPM·at block #6,791,550 · updates every 60s
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