Block #1,226,043

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/7/2015, 1:57:17 PM · Difficulty 10.7372 · 5,590,631 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c9444de3b08fd62773f112268ccc2872800d5a367644d93e6170932db4662980

Height

#1,226,043

Difficulty

10.737223

Transactions

5

Size

5.99 KB

Version

2

Bits

0abcbaa4

Nonce

443,493,702

Timestamp

9/7/2015, 1:57:17 PM

Confirmations

5,590,631

Merkle Root

e82594f9629bab5b98e37b37ee8c3f40d7a5869e00651dd3cb321bdf131e457b
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.

3.226 × 10⁹²(93-digit number)
32260981100331582315…54338618937661435681
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
3.226 × 10⁹²(93-digit number)
32260981100331582315…54338618937661435681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.452 × 10⁹²(93-digit number)
64521962200663164631…08677237875322871361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.290 × 10⁹³(94-digit number)
12904392440132632926…17354475750645742721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.580 × 10⁹³(94-digit number)
25808784880265265852…34708951501291485441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.161 × 10⁹³(94-digit number)
51617569760530531705…69417903002582970881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.032 × 10⁹⁴(95-digit number)
10323513952106106341…38835806005165941761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.064 × 10⁹⁴(95-digit number)
20647027904212212682…77671612010331883521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.129 × 10⁹⁴(95-digit number)
41294055808424425364…55343224020663767041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.258 × 10⁹⁴(95-digit number)
82588111616848850728…10686448041327534081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.651 × 10⁹⁵(96-digit number)
16517622323369770145…21372896082655068161
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:57,777,510 XPM·at block #6,816,673 · updates every 60s
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