Block #83,255

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/26/2013, 12:43:56 AM · Difficulty 9.2694 · 6,709,207 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ffe857c436d4e8d3ef4b0a6e4d5174dd7d66481f363a9991d88f6c6e1c08a3f4

View on Chainz ↗

Height

#83,255

Difficulty

9.269354

Transactions

Size

1.20 KB

Version

Bits

0944f461

Nonce

171

Timestamp

7/26/2013, 12:43:56 AM

Confirmations

6,709,207

Merkle Root

ff5ec59ff11eabbe59323122d8d1fda4447fb1fa86fb5a73e9554920dd00c6d7

Transactions (4)

Coinbase4ae7144dd6d23c…cecc32edc39d77

1 in → 1 out11.6500 XPM110 B

AKLV23VV…xUT1iYY9

7e82fb2de052c0…6c3035ffe2eb5d

3 in → 1 out740.7513 XPM455 B

AMzb1XrX…59PD7jsG

42be155d1d127d…9d421d96b82516

2 in → 2 out104.2059 XPM375 B

AZ4QWCHn…Ph4c1FrR AKZHGNpJ…FByhphHp

8eed8fe1291181…240fc82ef180d6

1 in → 1 out4.3400 XPM192 B

AHi48czA…v5pQ3cJ6

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.

7.078 × 10¹⁰²(103-digit number)

70780026309382246443…52528478829333851931

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.

origin + 1

7.078 × 10¹⁰²(103-digit number)

70780026309382246443…52528478829333851931

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.415 × 10¹⁰³(104-digit number)

14156005261876449288…05056957658667703861

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.831 × 10¹⁰³(104-digit number)

28312010523752898577…10113915317335407721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.662 × 10¹⁰³(104-digit number)

56624021047505797154…20227830634670815441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.132 × 10¹⁰⁴(105-digit number)

11324804209501159430…40455661269341630881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.264 × 10¹⁰⁴(105-digit number)

22649608419002318861…80911322538683261761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.529 × 10¹⁰⁴(105-digit number)

45299216838004637723…61822645077366523521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.059 × 10¹⁰⁴(105-digit number)

90598433676009275447…23645290154733047041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.811 × 10¹⁰⁵(106-digit number)

18119686735201855089…47290580309466094081

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, …

Cross-reference on Chainz Explorer