Block #60,267

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 7:01:10 AM · Difficulty 8.9685 · 6,734,678 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fe144b9009f316e90eea7fa2a66bf1d8f41780618a0170a76c16e6615f034d6b

Height

#60,267

Difficulty

8.968506

Transactions

2

Size

722 B

Version

2

Bits

08f7f008

Nonce

524

Timestamp

7/18/2013, 7:01:10 AM

Confirmations

6,734,678

Merkle Root

dac81f586a21190033680144622c13e232e8457c60ceb188873f7350fe64a466
Transactions (2)
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.

2.965 × 10¹⁰⁰(101-digit number)
29659595710175194082…23497957363365900001
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
2.965 × 10¹⁰⁰(101-digit number)
29659595710175194082…23497957363365900001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.931 × 10¹⁰⁰(101-digit number)
59319191420350388164…46995914726731800001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.186 × 10¹⁰¹(102-digit number)
11863838284070077632…93991829453463600001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.372 × 10¹⁰¹(102-digit number)
23727676568140155265…87983658906927200001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.745 × 10¹⁰¹(102-digit number)
47455353136280310531…75967317813854400001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.491 × 10¹⁰¹(102-digit number)
94910706272560621063…51934635627708800001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.898 × 10¹⁰²(103-digit number)
18982141254512124212…03869271255417600001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.796 × 10¹⁰²(103-digit number)
37964282509024248425…07738542510835200001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.592 × 10¹⁰²(103-digit number)
75928565018048496850…15477085021670400001
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:57,603,596 XPM·at block #6,794,944 · updates every 60s
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