Block #304,896

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2013, 4:27:10 AM · Difficulty 9.9935 · 6,500,969 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5bd00bba26a0c268b16084e2c6b8a55d0257b6e5f310bae21fe0320d81036118

Height

#304,896

Difficulty

9.993471

Transactions

2

Size

1.38 KB

Version

2

Bits

09fe5421

Nonce

143,090

Timestamp

12/11/2013, 4:27:10 AM

Confirmations

6,500,969

Merkle Root

9cd42c03f2b3270bd671224077bf1d1f9d0e6c800291fbcb231e6d19467729ce
Transactions (2)
1 in → 1 out10.0200 XPM110 B
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.

1.447 × 10⁹⁶(97-digit number)
14476404606111570882…32885015263800080001
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.

1
origin + 1
1.447 × 10⁹⁶(97-digit number)
14476404606111570882…32885015263800080001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.895 × 10⁹⁶(97-digit number)
28952809212223141764…65770030527600160001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.790 × 10⁹⁶(97-digit number)
57905618424446283528…31540061055200320001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.158 × 10⁹⁷(98-digit number)
11581123684889256705…63080122110400640001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.316 × 10⁹⁷(98-digit number)
23162247369778513411…26160244220801280001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.632 × 10⁹⁷(98-digit number)
46324494739557026822…52320488441602560001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.264 × 10⁹⁷(98-digit number)
92648989479114053645…04640976883205120001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.852 × 10⁹⁸(99-digit number)
18529797895822810729…09281953766410240001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.705 × 10⁹⁸(99-digit number)
37059595791645621458…18563907532820480001
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Circulating Supply:57,691,003 XPM·at block #6,805,864 · updates every 60s
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