Block #1,149,768

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/11/2015, 2:40:31 AM · Difficulty 10.9440 · 5,655,292 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a021203992c0d165ec69650dcf61ea2f3ab8b276ff9788978078076621678b08

Height

#1,149,768

Difficulty

10.944042

Transactions

3

Size

652 B

Version

2

Bits

0af1acb9

Nonce

865,853,321

Timestamp

7/11/2015, 2:40:31 AM

Confirmations

5,655,292

Merkle Root

0c4ffec3de81fdc4f18210bcc196d04fd8e4266551d7afb91c66e117be8795ab
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.

1.191 × 10⁹⁶(97-digit number)
11914175598872304397…71567106700499991041
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
1.191 × 10⁹⁶(97-digit number)
11914175598872304397…71567106700499991041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.382 × 10⁹⁶(97-digit number)
23828351197744608794…43134213400999982081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.765 × 10⁹⁶(97-digit number)
47656702395489217589…86268426801999964161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.531 × 10⁹⁶(97-digit number)
95313404790978435178…72536853603999928321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.906 × 10⁹⁷(98-digit number)
19062680958195687035…45073707207999856641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.812 × 10⁹⁷(98-digit number)
38125361916391374071…90147414415999713281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.625 × 10⁹⁷(98-digit number)
76250723832782748142…80294828831999426561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.525 × 10⁹⁸(99-digit number)
15250144766556549628…60589657663998853121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.050 × 10⁹⁸(99-digit number)
30500289533113099257…21179315327997706241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.100 × 10⁹⁸(99-digit number)
61000579066226198514…42358630655995412481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.220 × 10⁹⁹(100-digit number)
12200115813245239702…84717261311990824961
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:57,684,546 XPM·at block #6,805,059 · updates every 60s
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