Block #238,944

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/1/2013, 7:41:22 PM · Difficulty 9.9536 · 6,570,282 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00b1eb92fdc4540a417e2180c5a5e38514bc304c284d867f95d62da77f37c33f

Height

#238,944

Difficulty

9.953617

Transactions

3

Size

698 B

Version

2

Bits

09f42044

Nonce

146,179

Timestamp

11/1/2013, 7:41:22 PM

Confirmations

6,570,282

Merkle Root

1c36beb6428ff2ffee8f5c984014370312e47e95fb2b8e62b5d84f42aec87edb
Transactions (3)
1 in → 1 out10.1000 XPM109 B
1 in → 1 out10.1300 XPM158 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.

1.197 × 10⁹⁸(99-digit number)
11974089967103656592…12406369856247657601
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
1.197 × 10⁹⁸(99-digit number)
11974089967103656592…12406369856247657601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.394 × 10⁹⁸(99-digit number)
23948179934207313185…24812739712495315201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.789 × 10⁹⁸(99-digit number)
47896359868414626371…49625479424990630401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.579 × 10⁹⁸(99-digit number)
95792719736829252742…99250958849981260801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.915 × 10⁹⁹(100-digit number)
19158543947365850548…98501917699962521601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.831 × 10⁹⁹(100-digit number)
38317087894731701097…97003835399925043201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.663 × 10⁹⁹(100-digit number)
76634175789463402194…94007670799850086401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.532 × 10¹⁰⁰(101-digit number)
15326835157892680438…88015341599700172801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.065 × 10¹⁰⁰(101-digit number)
30653670315785360877…76030683199400345601
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:57,717,871 XPM·at block #6,809,225 · updates every 60s
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