Block #358,706

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/14/2014, 7:12:46 AM · Difficulty 10.3848 · 6,453,967 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

329c37864403d6b864ff26d65f2342f3e43a8d7399b97ef64f5540b4098fbbc5

View on Chainz ↗

Height

#358,706

Difficulty

10.384786

Transactions

Size

1.04 KB

Version

Bits

0a62815e

Nonce

32,515

Timestamp

1/14/2014, 7:12:46 AM

Confirmations

6,453,967

Mined by

⛏️ 2yaRYAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f2f74c36b05fac495d2e75f96dbc2515bac8f1f62e72fec4188c3728ac6cbf79

Transactions (1)

Coinbasef2f74c36b05fac…8c3728ac6cbf79

1 in → 27 out9.2600 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AXmS7tZu…11YypHLP AJzWx2VD…j4ZSMit5

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.

7.550 × 10⁹²(93-digit number)

75506924942917008576…51451769839183495799

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

7.550 × 10⁹²(93-digit number)

75506924942917008576…51451769839183495799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.510 × 10⁹³(94-digit number)

15101384988583401715…02903539678366991599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.020 × 10⁹³(94-digit number)

30202769977166803430…05807079356733983199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.040 × 10⁹³(94-digit number)

60405539954333606861…11614158713467966399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.208 × 10⁹⁴(95-digit number)

12081107990866721372…23228317426935932799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.416 × 10⁹⁴(95-digit number)

24162215981733442744…46456634853871865599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.832 × 10⁹⁴(95-digit number)

48324431963466885488…92913269707743731199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.664 × 10⁹⁴(95-digit number)

96648863926933770977…85826539415487462399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.932 × 10⁹⁵(96-digit number)

19329772785386754195…71653078830974924799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.865 × 10⁹⁵(96-digit number)

38659545570773508391…43306157661949849599

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 #358,706

Cookie Preferences