Block #59,855

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2013, 4:42:11 AM · Difficulty 8.9667 · 6,729,927 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8689c5a0b90e8bce1c8ddf954034f25a3b4f5fc69274168d9d7e92714e845ac7

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Height

#59,855

Difficulty

8.966738

Transactions

Size

1.28 KB

Version

Bits

08f77c28

Nonce

203

Timestamp

7/18/2013, 4:42:11 AM

Confirmations

6,729,927

Merkle Root

fe51361866531b2282e49915cd155676161cb4ef789be535f858dc34269048e6

Transactions (3)

Coinbase672d532ea81fa9…e193efbaf3c5b7

1 in → 1 out12.4400 XPM110 B

Ab49LBLN…mEhZvW9v

8168d968094fd3…297702d06fa754

5 in → 1 out62.3600 XPM612 B

ANLm86MU…cjLmdcRw

ca5a8586db3fc2…fcc10b10d969f4

3 in → 2 out40.0100 XPM491 B

AJgTtr6m…Rg5ATvYs AeFbzyLv…uL8iw1RZ

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.

6.463 × 10¹¹⁴(115-digit number)

64631377450634116617…20391402364193864019

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

6.463 × 10¹¹⁴(115-digit number)

64631377450634116617…20391402364193864019

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.292 × 10¹¹⁵(116-digit number)

12926275490126823323…40782804728387728039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.585 × 10¹¹⁵(116-digit number)

25852550980253646646…81565609456775456079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.170 × 10¹¹⁵(116-digit number)

51705101960507293293…63131218913550912159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.034 × 10¹¹⁶(117-digit number)

10341020392101458658…26262437827101824319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.068 × 10¹¹⁶(117-digit number)

20682040784202917317…52524875654203648639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.136 × 10¹¹⁶(117-digit number)

41364081568405834635…05049751308407297279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.272 × 10¹¹⁶(117-digit number)

82728163136811669270…10099502616814594559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.654 × 10¹¹⁷(118-digit number)

16545632627362333854…20199005233629189119

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