Block #1,238,188

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/15/2015, 5:41:00 PM · Difficulty 10.7577 · 5,595,296 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6215ba6bdf33c09747c8fc7b9d181eef050ef90d2e584a87739c190431ad677f

Height

#1,238,188

Difficulty

10.757654

Transactions

3

Size

955 B

Version

2

Bits

0ac1f599

Nonce

423,219,116

Timestamp

9/15/2015, 5:41:00 PM

Confirmations

5,595,296

Merkle Root

8d7c018574d6eeee88626d9b9eca9f8d3795a8bd5e01181a485f1b0b7894511e
Transactions (3)
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.

2.997 × 10⁹⁶(97-digit number)
29977746331641780771…10053154959782506881
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
2.997 × 10⁹⁶(97-digit number)
29977746331641780771…10053154959782506881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.995 × 10⁹⁶(97-digit number)
59955492663283561543…20106309919565013761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.199 × 10⁹⁷(98-digit number)
11991098532656712308…40212619839130027521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.398 × 10⁹⁷(98-digit number)
23982197065313424617…80425239678260055041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.796 × 10⁹⁷(98-digit number)
47964394130626849235…60850479356520110081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.592 × 10⁹⁷(98-digit number)
95928788261253698470…21700958713040220161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.918 × 10⁹⁸(99-digit number)
19185757652250739694…43401917426080440321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.837 × 10⁹⁸(99-digit number)
38371515304501479388…86803834852160880641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.674 × 10⁹⁸(99-digit number)
76743030609002958776…73607669704321761281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.534 × 10⁹⁹(100-digit number)
15348606121800591755…47215339408643522561
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:57,912,076 XPM·at block #6,833,483 · updates every 60s
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