Block #214,950

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/17/2013, 7:05:46 PM · Difficulty 9.9246 · 6,595,764 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d5bf792733cb4164c63ddccc395656d75124c51d1963ca861ff2117fce8067fc

Height

#214,950

Difficulty

9.924560

Transactions

1

Size

5.46 KB

Version

2

Bits

09ecaff9

Nonce

1,164,792,131

Timestamp

10/17/2013, 7:05:46 PM

Confirmations

6,595,764

Merkle Root

a1c7ca62f68a3db783e34d53ecc277ae141665247cbcf35fa8ede6859c48b3c2
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.

1.038 × 10⁹⁵(96-digit number)
10385406916737942103…14458498729106784561
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
1.038 × 10⁹⁵(96-digit number)
10385406916737942103…14458498729106784561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.077 × 10⁹⁵(96-digit number)
20770813833475884207…28916997458213569121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.154 × 10⁹⁵(96-digit number)
41541627666951768414…57833994916427138241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.308 × 10⁹⁵(96-digit number)
83083255333903536828…15667989832854276481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.661 × 10⁹⁶(97-digit number)
16616651066780707365…31335979665708552961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.323 × 10⁹⁶(97-digit number)
33233302133561414731…62671959331417105921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.646 × 10⁹⁶(97-digit number)
66466604267122829462…25343918662834211841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.329 × 10⁹⁷(98-digit number)
13293320853424565892…50687837325668423681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.658 × 10⁹⁷(98-digit number)
26586641706849131784…01375674651336847361
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:57,729,799 XPM·at block #6,810,713 · updates every 60s
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