Block #1,116,367

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/18/2015, 8:29:16 PM · Difficulty 10.9257 · 5,697,994 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ee2d3893613bf22454cf2218809e096402308d6eab617506681773bc7887ff78

Height

#1,116,367

Difficulty

10.925721

Transactions

2

Size

539 B

Version

2

Bits

0aecfc0c

Nonce

374,345,913

Timestamp

6/18/2015, 8:29:16 PM

Confirmations

5,697,994

Merkle Root

73941cf613af15bdb7f09a2fadcda7671feb84f80769de60734411cdd76cfd0b
Transactions (2)
1 in → 1 out8.3700 XPM110 B
2 in → 1 out214.1877 XPM340 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.

5.615 × 10⁹²(93-digit number)
56159103124843429451…53272370572711555201
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
5.615 × 10⁹²(93-digit number)
56159103124843429451…53272370572711555201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.123 × 10⁹³(94-digit number)
11231820624968685890…06544741145423110401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.246 × 10⁹³(94-digit number)
22463641249937371780…13089482290846220801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.492 × 10⁹³(94-digit number)
44927282499874743561…26178964581692441601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.985 × 10⁹³(94-digit number)
89854564999749487122…52357929163384883201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.797 × 10⁹⁴(95-digit number)
17970912999949897424…04715858326769766401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.594 × 10⁹⁴(95-digit number)
35941825999899794848…09431716653539532801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.188 × 10⁹⁴(95-digit number)
71883651999799589697…18863433307079065601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.437 × 10⁹⁵(96-digit number)
14376730399959917939…37726866614158131201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.875 × 10⁹⁵(96-digit number)
28753460799919835879…75453733228316262401
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:57,758,954 XPM·at block #6,814,360 · updates every 60s
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