Block #79,606

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/23/2013, 2:44:31 PM · Difficulty 9.2437 · 6,714,704 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d840bc4abe4a5bf0ee31efe3108790a6a537562ddcd3ddf75b19b1173d189556

View on Chainz ↗

Height

#79,606

Difficulty

9.243726

Transactions

Size

840 B

Version

Bits

093e64d1

Nonce

85,032

Timestamp

7/23/2013, 2:44:31 PM

Confirmations

6,714,704

Merkle Root

8a068189a2120c0b93cc50b3137d46d7d33c6a912a0bfecb8626e4c4ab70f990

Transactions (2)

Coinbase8ea2169e473f15…37b4f65dd6085a

1 in → 1 out11.7000 XPM109 B

AMRJBb3V…Zv15uY6D

517608371f909a…4946ce34f4f2db

4 in → 1 out3000.0000 XPM638 B

AQHTR3Ji…faYBg5P8

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.

3.156 × 10¹⁰¹(102-digit number)

31562557665804161996…22690750418473870739

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

3.156 × 10¹⁰¹(102-digit number)

31562557665804161996…22690750418473870739

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.312 × 10¹⁰¹(102-digit number)

63125115331608323992…45381500836947741479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.262 × 10¹⁰²(103-digit number)

12625023066321664798…90763001673895482959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.525 × 10¹⁰²(103-digit number)

25250046132643329596…81526003347790965919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.050 × 10¹⁰²(103-digit number)

50500092265286659193…63052006695581931839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.010 × 10¹⁰³(104-digit number)

10100018453057331838…26104013391163863679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.020 × 10¹⁰³(104-digit number)

20200036906114663677…52208026782327727359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.040 × 10¹⁰³(104-digit number)

40400073812229327355…04416053564655454719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.080 × 10¹⁰³(104-digit number)

80800147624458654710…08832107129310909439

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