Block #60,991

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2013, 11:01:18 AM · Difficulty 8.9714 · 6,728,949 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2c1fed26460f358577dfee491c02119e4e162e218164e5bf82743c81440c6965

View on Chainz ↗

Height

#60,991

Difficulty

8.971437

Transactions

Size

1.33 KB

Version

Bits

08f8b01e

Nonce

2,011

Timestamp

7/18/2013, 11:01:18 AM

Confirmations

6,728,949

Merkle Root

b0b2ff5af19beb1a07553e0042855de8b3190ec34847e1de5ffbd80ecfc870bf

Transactions (3)

Coinbase220f4db7d2b79b…c65d9f787fceca

1 in → 1 out12.4300 XPM109 B

AK1JUKWL…oPR4rN5o

4d23d327095f29…b9705cd9a3f92b

2 in → 2 out12.6600 XPM340 B

AdSs4NuX…igwomChz AdHH4S7H…YBpU1DpD

bef34c3d046ea5…7c99421a934851

5 in → 2 out100.0151 XPM818 B

AQmnChH7…iBjVSPm7 AZDGtMNV…LpCmGEpM

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.

4.946 × 10¹⁰³(104-digit number)

49461736369006403058…59423499524994486939

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

4.946 × 10¹⁰³(104-digit number)

49461736369006403058…59423499524994486939

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.892 × 10¹⁰³(104-digit number)

98923472738012806116…18846999049988973879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.978 × 10¹⁰⁴(105-digit number)

19784694547602561223…37693998099977947759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.956 × 10¹⁰⁴(105-digit number)

39569389095205122446…75387996199955895519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.913 × 10¹⁰⁴(105-digit number)

79138778190410244893…50775992399911791039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.582 × 10¹⁰⁵(106-digit number)

15827755638082048978…01551984799823582079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.165 × 10¹⁰⁵(106-digit number)

31655511276164097957…03103969599647164159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.331 × 10¹⁰⁵(106-digit number)

63311022552328195914…06207939199294328319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.266 × 10¹⁰⁶(107-digit number)

12662204510465639182…12415878398588656639

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