Block #965,789

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/9/2015, 6:03:55 AM · Difficulty 10.8223 · 5,830,225 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1251f14c3e21df9f201f1d731467a6b270f276f78556a7bba8a5c917549435b2

Height

#965,789

Difficulty

10.822323

Transactions

2

Size

580 B

Version

2

Bits

0ad283c1

Nonce

2,755,590

Timestamp

3/9/2015, 6:03:55 AM

Confirmations

5,830,225

Merkle Root

dab554a3fd797356ae20cf76057566148bb238b67575d3e7e8bce7d5a316233d
Transactions (2)
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.

1.325 × 10⁹⁷(98-digit number)
13253957635133648999…85944809575648008961
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
1.325 × 10⁹⁷(98-digit number)
13253957635133648999…85944809575648008961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.650 × 10⁹⁷(98-digit number)
26507915270267297998…71889619151296017921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.301 × 10⁹⁷(98-digit number)
53015830540534595997…43779238302592035841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.060 × 10⁹⁸(99-digit number)
10603166108106919199…87558476605184071681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.120 × 10⁹⁸(99-digit number)
21206332216213838399…75116953210368143361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.241 × 10⁹⁸(99-digit number)
42412664432427676798…50233906420736286721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.482 × 10⁹⁸(99-digit number)
84825328864855353596…00467812841472573441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.696 × 10⁹⁹(100-digit number)
16965065772971070719…00935625682945146881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.393 × 10⁹⁹(100-digit number)
33930131545942141438…01871251365890293761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.786 × 10⁹⁹(100-digit number)
67860263091884282877…03742502731780587521
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, …
Circulating Supply:57,612,203 XPM·at block #6,796,013 · updates every 60s
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