Block #207,696

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/13/2013, 2:22:12 PM · Difficulty 9.9036 · 6,602,491 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37a7fbf7bdf8d20d079f8c51fd458c9085b02e82e8ff0abb071c7db2f62ef13f

Height

#207,696

Difficulty

9.903632

Transactions

2

Size

722 B

Version

2

Bits

09e75472

Nonce

115,648

Timestamp

10/13/2013, 2:22:12 PM

Confirmations

6,602,491

Merkle Root

638e8419da74bb812f9dc40036f212a9caa2416a934d2a2d50dcf1f6e17ad8b0
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.

6.075 × 10⁹⁶(97-digit number)
60758075454498696028…68426003391995904001
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
6.075 × 10⁹⁶(97-digit number)
60758075454498696028…68426003391995904001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.215 × 10⁹⁷(98-digit number)
12151615090899739205…36852006783991808001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.430 × 10⁹⁷(98-digit number)
24303230181799478411…73704013567983616001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.860 × 10⁹⁷(98-digit number)
48606460363598956822…47408027135967232001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.721 × 10⁹⁷(98-digit number)
97212920727197913644…94816054271934464001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.944 × 10⁹⁸(99-digit number)
19442584145439582728…89632108543868928001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.888 × 10⁹⁸(99-digit number)
38885168290879165457…79264217087737856001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.777 × 10⁹⁸(99-digit number)
77770336581758330915…58528434175475712001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.555 × 10⁹⁹(100-digit number)
15554067316351666183…17056868350951424001
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:57,725,566 XPM·at block #6,810,186 · updates every 60s
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