Block #410,137

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/18/2014, 8:34:57 PM · Difficulty 10.4301 · 6,384,050 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ac0fc73992e82a8bdb5dd66798cf79fd39a8c4454bc68c74c4911def311876a7

View on Chainz ↗

Height

#410,137

Difficulty

10.430098

Transactions

Size

1.42 KB

Version

Bits

0a6e1adf

Nonce

52,448

Timestamp

2/18/2014, 8:34:57 PM

Confirmations

6,384,050

Merkle Root

59cebf9d8d4d5e730f3213be8fe345ae41d8c349ea16f55f43780c5306fed917

Transactions (2)

Coinbase48d57a274b3bb9…792057ce79dde7

1 in → 1 out9.1800 XPM97 B

AYCeLhqB…eqGM6KK1

29baec1d8a1a32…6ec210bd850e0b

8 in → 2 out7.0923 XPM1.23 KB

AQjG4qAu…yMqZJxNQ Ac8knWXR…uUMyn63E

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.

4.055 × 10¹⁰²(103-digit number)

40559783292374810561…82303986864458403839

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

4.055 × 10¹⁰²(103-digit number)

40559783292374810561…82303986864458403839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.111 × 10¹⁰²(103-digit number)

81119566584749621123…64607973728916807679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.622 × 10¹⁰³(104-digit number)

16223913316949924224…29215947457833615359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.244 × 10¹⁰³(104-digit number)

32447826633899848449…58431894915667230719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.489 × 10¹⁰³(104-digit number)

64895653267799696899…16863789831334461439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.297 × 10¹⁰⁴(105-digit number)

12979130653559939379…33727579662668922879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.595 × 10¹⁰⁴(105-digit number)

25958261307119878759…67455159325337845759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.191 × 10¹⁰⁴(105-digit number)

51916522614239757519…34910318650675691519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.038 × 10¹⁰⁵(106-digit number)

10383304522847951503…69820637301351383039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.076 × 10¹⁰⁵(106-digit number)

20766609045695903007…39641274602702766079

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