Block #142,927

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/31/2013, 7:22:03 AM · Difficulty 9.8374 · 6,651,954 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9a4bfa460151584c43912831edf3a83882bbad4f1800ac7572ce2ded0cd52a63

View on Chainz ↗

Height

#142,927

Difficulty

9.837383

Transactions

Size

426 B

Version

Bits

09d65ebf

Nonce

120,676

Timestamp

8/31/2013, 7:22:03 AM

Confirmations

6,651,954

Mined by

⛏️ P2SHAcuHyuDtQs9JHeKfPNWdE7yizjfg9uxern

Merkle Root

6e6de24f14b28e2f4c6a4f8a6eab0bdd50052d2d3513157fe8bba9f7dccbbe87

Transactions (2)

Coinbaseadcab6253ddacf…b84deda22bbf82

1 in → 1 out10.3300 XPM109 B

AcuHyuDt…fg9uxern

ef4a148d3807bd…eefae4f3a6e547

1 in → 2 out22.7500 XPM226 B

AFtap2en…4d4n6Nrg AQqXeoQ2…NUCHMg6m

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.

2.513 × 10⁹⁷(98-digit number)

25133172926951685915…48186540605844383999

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

2.513 × 10⁹⁷(98-digit number)

25133172926951685915…48186540605844383999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.026 × 10⁹⁷(98-digit number)

50266345853903371831…96373081211688767999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.005 × 10⁹⁸(99-digit number)

10053269170780674366…92746162423377535999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.010 × 10⁹⁸(99-digit number)

20106538341561348732…85492324846755071999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.021 × 10⁹⁸(99-digit number)

40213076683122697464…70984649693510143999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.042 × 10⁹⁸(99-digit number)

80426153366245394929…41969299387020287999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.608 × 10⁹⁹(100-digit number)

16085230673249078985…83938598774040575999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.217 × 10⁹⁹(100-digit number)

32170461346498157971…67877197548081151999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.434 × 10⁹⁹(100-digit number)

64340922692996315943…35754395096162303999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.286 × 10¹⁰⁰(101-digit number)

12868184538599263188…71508790192324607999

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