Block #73,164

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/21/2013, 4:19:02 AM · Difficulty 8.9946 · 6,718,254 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2bcdab67b491a77b403743da9ea78cd173f5f7d791e479563e2720666d4fc001

View on Chainz ↗

Height

#73,164

Difficulty

8.994624

Transactions

Size

203 B

Version

Bits

08fe9fb0

Nonce

783

Timestamp

7/21/2013, 4:19:02 AM

Confirmations

6,718,254

Merkle Root

c6278dbb74dcd8a721a1efee8e4099f2ddbe0f31a4292b1b3128b52f1211c62f

Transactions (1)

Coinbasec6278dbb74dcd8…28b52f1211c62f

1 in → 1 out12.3400 XPM110 B

ANCYL9xh…9WyGnqDE

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.

1.201 × 10¹⁰¹(102-digit number)

12014598653814981710…79292413876030474339

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

1.201 × 10¹⁰¹(102-digit number)

12014598653814981710…79292413876030474339

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.402 × 10¹⁰¹(102-digit number)

24029197307629963421…58584827752060948679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.805 × 10¹⁰¹(102-digit number)

48058394615259926843…17169655504121897359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.611 × 10¹⁰¹(102-digit number)

96116789230519853687…34339311008243794719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.922 × 10¹⁰²(103-digit number)

19223357846103970737…68678622016487589439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.844 × 10¹⁰²(103-digit number)

38446715692207941474…37357244032975178879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.689 × 10¹⁰²(103-digit number)

76893431384415882949…74714488065950357759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.537 × 10¹⁰³(104-digit number)

15378686276883176589…49428976131900715519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.075 × 10¹⁰³(104-digit number)

30757372553766353179…98857952263801431039

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