Block #508,357

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/24/2014, 8:22:58 AM · Difficulty 10.8181 · 6,299,268 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

72276f4c7ea552f249351e4e1c0fa734b6d1d6e56a2f56552d4c15e868b50af8

View on Chainz ↗

Height

#508,357

Difficulty

10.818114

Transactions

Size

731 B

Version

Bits

0ad16ff0

Nonce

177,464

Timestamp

4/24/2014, 8:22:58 AM

Confirmations

6,299,268

Mined by

⛏️ aSX9ATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

6178a5910477102e037ca6b32ce9d51e7438bbf07b4ef0e1e2a931a42771fd5c

Transactions (1)

Coinbase6178a591047710…a931a42771fd5c

1 in → 17 out8.5300 XPM641 B

ATKK7iFz…wZm46KN1 AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AJtNW28X…Syb4Ph5j AdxPNkWD…ZMa9u34q

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.

6.386 × 10⁹³(94-digit number)

63869354930755058441…00322589145289721281

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

6.386 × 10⁹³(94-digit number)

63869354930755058441…00322589145289721281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.277 × 10⁹⁴(95-digit number)

12773870986151011688…00645178290579442561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.554 × 10⁹⁴(95-digit number)

25547741972302023376…01290356581158885121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.109 × 10⁹⁴(95-digit number)

51095483944604046753…02580713162317770241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.021 × 10⁹⁵(96-digit number)

10219096788920809350…05161426324635540481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.043 × 10⁹⁵(96-digit number)

20438193577841618701…10322852649271080961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.087 × 10⁹⁵(96-digit number)

40876387155683237402…20645705298542161921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.175 × 10⁹⁵(96-digit number)

81752774311366474805…41291410597084323841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.635 × 10⁹⁶(97-digit number)

16350554862273294961…82582821194168647681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.270 × 10⁹⁶(97-digit number)

32701109724546589922…65165642388337295361

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #508,357

Cookie Preferences