Block #60,309

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 7:16:23 AM · Difficulty 8.9687 · 6,731,171 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9f2f8adaa355b68ced3346722c9962aae801fb539f7a869d5d1134155a07b380

Height

#60,309

Difficulty

8.968673

Transactions

2

Size

5.12 KB

Version

2

Bits

08f7faf3

Nonce

91

Timestamp

7/18/2013, 7:16:23 AM

Confirmations

6,731,171

Merkle Root

553d26e56904125920b5914b60fbeafaea05c3df3434119d4d18247fd2417290
Transactions (2)
1 in → 1 out12.4700 XPM110 B
34 in → 1 out500.0000 XPM4.92 KB
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.

7.283 × 10⁹⁴(95-digit number)
72830741916297378156…30115656137347646501
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
7.283 × 10⁹⁴(95-digit number)
72830741916297378156…30115656137347646501
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.456 × 10⁹⁵(96-digit number)
14566148383259475631…60231312274695293001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.913 × 10⁹⁵(96-digit number)
29132296766518951262…20462624549390586001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.826 × 10⁹⁵(96-digit number)
58264593533037902525…40925249098781172001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.165 × 10⁹⁶(97-digit number)
11652918706607580505…81850498197562344001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.330 × 10⁹⁶(97-digit number)
23305837413215161010…63700996395124688001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.661 × 10⁹⁶(97-digit number)
46611674826430322020…27401992790249376001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.322 × 10⁹⁶(97-digit number)
93223349652860644040…54803985580498752001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.864 × 10⁹⁷(98-digit number)
18644669930572128808…09607971160997504001
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:57,575,778 XPM·at block #6,791,479 · updates every 60s
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