Block #1,212,451

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/28/2015, 11:01:17 PM · Difficulty 10.7500 · 5,629,578 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3154126ef3d702af2077d5bc95ee7b80ba0e06eea186f121aadbc05be421f3b6

Height

#1,212,451

Difficulty

10.750026

Transactions

2

Size

435 B

Version

2

Bits

0ac001b4

Nonce

221,312,546

Timestamp

8/28/2015, 11:01:17 PM

Confirmations

5,629,578

Merkle Root

d67bb531396935b65ff8e20f25ce05d58ed706927bfd88db00e24ff84595574d
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.

3.311 × 10⁹⁸(99-digit number)
33112108370958338549…00895645363398041601
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
3.311 × 10⁹⁸(99-digit number)
33112108370958338549…00895645363398041601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.622 × 10⁹⁸(99-digit number)
66224216741916677099…01791290726796083201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.324 × 10⁹⁹(100-digit number)
13244843348383335419…03582581453592166401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.648 × 10⁹⁹(100-digit number)
26489686696766670839…07165162907184332801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.297 × 10⁹⁹(100-digit number)
52979373393533341679…14330325814368665601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.059 × 10¹⁰⁰(101-digit number)
10595874678706668335…28660651628737331201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.119 × 10¹⁰⁰(101-digit number)
21191749357413336671…57321303257474662401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.238 × 10¹⁰⁰(101-digit number)
42383498714826673343…14642606514949324801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.476 × 10¹⁰⁰(101-digit number)
84766997429653346687…29285213029898649601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.695 × 10¹⁰¹(102-digit number)
16953399485930669337…58570426059797299201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.390 × 10¹⁰¹(102-digit number)
33906798971861338675…17140852119594598401
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,980,619 XPM·at block #6,842,028 · updates every 60s
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