Block #77,634

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/22/2013, 12:02:06 PM · Difficulty 9.1860 · 6,715,141 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f279e8fc3a20ceb917e04ca4cc230e96a68d2df5e274f1352055a0afa2a83dbf

View on Chainz ↗

Height

#77,634

Difficulty

9.185982

Transactions

Size

1.66 KB

Version

Bits

092f9c86

Nonce

Timestamp

7/22/2013, 12:02:06 PM

Confirmations

6,715,141

Merkle Root

fb9e339e4a53f44584496696287c74b574f0319c2a79ffe370c0e7c2c1931018

Transactions (4)

Coinbaseb8abbd52720bfe…f6c73fd539bc20

1 in → 1 out11.8600 XPM110 B

AY7bbgtu…6faXcaqm

1f9d247b399557…1d72e7e52ca8eb

5 in → 2 out3226.6883 XPM818 B

AToNe3Uz…i4t5oTJd AK5pCNa1…W5o9bxM6

0ee96ddfe5de9d…134f7201d02dcd

1 in → 1 out12.3600 XPM158 B

AJRjXpzf…j56hFQFY

041c776355ff62…fb1301a93ea3b2

3 in → 2 out100.0129 XPM524 B

AMhSsZ9U…TgmkQEfq ATk7bHnG…Xb8euRQv

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.

1.406 × 10¹⁰³(104-digit number)

14069373300031394731…35819548136871671429

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

1.406 × 10¹⁰³(104-digit number)

14069373300031394731…35819548136871671429

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.813 × 10¹⁰³(104-digit number)

28138746600062789462…71639096273743342859

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.627 × 10¹⁰³(104-digit number)

56277493200125578924…43278192547486685719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.125 × 10¹⁰⁴(105-digit number)

11255498640025115784…86556385094973371439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.251 × 10¹⁰⁴(105-digit number)

22510997280050231569…73112770189946742879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.502 × 10¹⁰⁴(105-digit number)

45021994560100463139…46225540379893485759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.004 × 10¹⁰⁴(105-digit number)

90043989120200926278…92451080759786971519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.800 × 10¹⁰⁵(106-digit number)

18008797824040185255…84902161519573943039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.601 × 10¹⁰⁵(106-digit number)

36017595648080370511…69804323039147886079

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer