Block #270,117

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/23/2013, 5:18:22 PM · Difficulty 9.9519 · 6,521,334 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

50c327f3d6b0b84726c22540957659e4c5e16fdf23bfd34f55d0ac3771b91302

View on Chainz ↗

Height

#270,117

Difficulty

9.951871

Transactions

Size

610 B

Version

Bits

09f3adca

Nonce

2,193

Timestamp

11/23/2013, 5:18:22 PM

Confirmations

6,521,334

Merkle Root

79b6c4c98dd22151afe2461f9fe69ac334fa0cbea3caad5e0c7fefea5434ec2e

Transactions (2)

Coinbase77477e2f7a260a…84d45006783b5c

1 in → 2 out10.0900 XPM141 B

AdGRRh1e…QmctLb24 AHsw4d6U…EnM8UXNZ

d3dac94bfe9132…b46628a02da32a

2 in → 2 out299.9900 XPM375 B

AXbSp9ay…VrdQ3YKx ARTj8Sht…mzEACKC1

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.

3.777 × 10¹⁰³(104-digit number)

37775482673645907699…53169372570532268639

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

3.777 × 10¹⁰³(104-digit number)

37775482673645907699…53169372570532268639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.555 × 10¹⁰³(104-digit number)

75550965347291815399…06338745141064537279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.511 × 10¹⁰⁴(105-digit number)

15110193069458363079…12677490282129074559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.022 × 10¹⁰⁴(105-digit number)

30220386138916726159…25354980564258149119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.044 × 10¹⁰⁴(105-digit number)

60440772277833452319…50709961128516298239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.208 × 10¹⁰⁵(106-digit number)

12088154455566690463…01419922257032596479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.417 × 10¹⁰⁵(106-digit number)

24176308911133380927…02839844514065192959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.835 × 10¹⁰⁵(106-digit number)

48352617822266761855…05679689028130385919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.670 × 10¹⁰⁵(106-digit number)

96705235644533523710…11359378056260771839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.934 × 10¹⁰⁶(107-digit number)

19341047128906704742…22718756112521543679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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