Block #350,920

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/9/2014, 9:02:44 AM · Difficulty 10.2897 · 6,452,740 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

66756f4f5b5e77e01d1a4020d53c8922ba99f10e3fc8a3ad8d7e017fe4c79b87

View on Chainz ↗

Height

#350,920

Difficulty

10.289724

Transactions

Size

1.08 KB

Version

Bits

0a4a2b54

Nonce

10,722

Timestamp

1/9/2014, 9:02:44 AM

Confirmations

6,452,740

Mined by

⛏️ ZaRfAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e221d98323715af53931ee7e551055a348641fd29023aa7735c466c7d980add9

Transactions (1)

Coinbasee221d98323715a…c466c7d980add9

1 in → 28 out9.4100 XPM1015 B

AQvZBsUo…hppgRZTJ AUnkFe8H…fvenjA4X AZV4TwxQ…8JnQqSoH AXeQnyEs…fUWKQwq8 AH3Qkpre…d9jSDwSX

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.

9.623 × 10⁹⁶(97-digit number)

96234664201798707889…15068083233585890359

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

9.623 × 10⁹⁶(97-digit number)

96234664201798707889…15068083233585890359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.924 × 10⁹⁷(98-digit number)

19246932840359741577…30136166467171780719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.849 × 10⁹⁷(98-digit number)

38493865680719483155…60272332934343561439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.698 × 10⁹⁷(98-digit number)

76987731361438966311…20544665868687122879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.539 × 10⁹⁸(99-digit number)

15397546272287793262…41089331737374245759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.079 × 10⁹⁸(99-digit number)

30795092544575586524…82178663474748491519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.159 × 10⁹⁸(99-digit number)

61590185089151173049…64357326949496983039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.231 × 10⁹⁹(100-digit number)

12318037017830234609…28714653898993966079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.463 × 10⁹⁹(100-digit number)

24636074035660469219…57429307797987932159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.927 × 10⁹⁹(100-digit number)

49272148071320938439…14858615595975864319

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