Block #1,345,827

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/28/2015, 12:20:54 PM · Difficulty 10.8202 · 5,499,530 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e293429b708bbd5cd91465051a60d40b992abb3bead410997bc59d16061582d6

View on Chainz ↗

Height

#1,345,827

Difficulty

10.820155

Transactions

Size

243 B

Version

Bits

0ad1f5ad

Nonce

511,757,010

Timestamp

11/28/2015, 12:20:54 PM

Confirmations

5,499,530

Mined by

⛏️ P2SHASetrRSkYtcpqwkt2DDbeb53YJNKZtBfbV

Merkle Root

b5aa02b39e0ae0ad2225a48b2155c4155e26aad3d5a79546d6873353fd761c8a

Transactions (1)

Coinbaseb5aa02b39e0ae0…873353fd761c8a

1 in → 2 out8.5300 XPM152 B

ASetrRSk…NKZtBfbV ALPu3s2c…EJXLjVFh

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.

2.128 × 10⁹⁷(98-digit number)

21287186371859937636…52203690817152527359

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

2.128 × 10⁹⁷(98-digit number)

21287186371859937636…52203690817152527359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.257 × 10⁹⁷(98-digit number)

42574372743719875273…04407381634305054719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.514 × 10⁹⁷(98-digit number)

85148745487439750546…08814763268610109439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.702 × 10⁹⁸(99-digit number)

17029749097487950109…17629526537220218879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.405 × 10⁹⁸(99-digit number)

34059498194975900218…35259053074440437759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.811 × 10⁹⁸(99-digit number)

68118996389951800437…70518106148880875519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.362 × 10⁹⁹(100-digit number)

13623799277990360087…41036212297761751039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.724 × 10⁹⁹(100-digit number)

27247598555980720174…82072424595523502079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.449 × 10⁹⁹(100-digit number)

54495197111961440349…64144849191047004159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.089 × 10¹⁰⁰(101-digit number)

10899039422392288069…28289698382094008319

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

Block #1,345,827

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