Block #914,032

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/29/2015, 2:41:50 AM · Difficulty 10.9271 · 5,882,233 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
096912a52000eb63fe76ca28a2c7c1d7b57737fa887aa8c818a67a00504baffa

Height

#914,032

Difficulty

10.927120

Transactions

5

Size

15.67 KB

Version

2

Bits

0aed57c1

Nonce

112,414,202

Timestamp

1/29/2015, 2:41:50 AM

Confirmations

5,882,233

Merkle Root

e8d7e66ea028725ad7598f446fe30bb37ce944355d65228c101a59b115a106a1
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.

1.105 × 10⁹⁴(95-digit number)
11052576313704476466…51768328761687512681
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
1.105 × 10⁹⁴(95-digit number)
11052576313704476466…51768328761687512681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.210 × 10⁹⁴(95-digit number)
22105152627408952932…03536657523375025361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.421 × 10⁹⁴(95-digit number)
44210305254817905865…07073315046750050721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.842 × 10⁹⁴(95-digit number)
88420610509635811730…14146630093500101441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.768 × 10⁹⁵(96-digit number)
17684122101927162346…28293260187000202881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.536 × 10⁹⁵(96-digit number)
35368244203854324692…56586520374000405761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.073 × 10⁹⁵(96-digit number)
70736488407708649384…13173040748000811521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.414 × 10⁹⁶(97-digit number)
14147297681541729876…26346081496001623041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.829 × 10⁹⁶(97-digit number)
28294595363083459753…52692162992003246081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.658 × 10⁹⁶(97-digit number)
56589190726166919507…05384325984006492161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.131 × 10⁹⁷(98-digit number)
11317838145233383901…10768651968012984321
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:57,614,119 XPM·at block #6,796,264 · updates every 60s
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