Block #937,368

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/15/2015, 10:30:47 AM · Difficulty 10.9007 · 5,863,332 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a9f115bc34722e6af51b7213b12ea55ceeadaefcfa17e3f521ac764ca950cdb4

Height

#937,368

Difficulty

10.900688

Transactions

5

Size

1.09 KB

Version

2

Bits

0ae69384

Nonce

273,568,345

Timestamp

2/15/2015, 10:30:47 AM

Confirmations

5,863,332

Merkle Root

7a857ae5ea3b12ce757cecd47c49848e7f495657fa9f9d74e44ce92e460faf85
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.

1.202 × 10⁹⁷(98-digit number)
12028113470770479036…28553751277345122559
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
1.202 × 10⁹⁷(98-digit number)
12028113470770479036…28553751277345122559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.405 × 10⁹⁷(98-digit number)
24056226941540958072…57107502554690245119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.811 × 10⁹⁷(98-digit number)
48112453883081916144…14215005109380490239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.622 × 10⁹⁷(98-digit number)
96224907766163832289…28430010218760980479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.924 × 10⁹⁸(99-digit number)
19244981553232766457…56860020437521960959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.848 × 10⁹⁸(99-digit number)
38489963106465532915…13720040875043921919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.697 × 10⁹⁸(99-digit number)
76979926212931065831…27440081750087843839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.539 × 10⁹⁹(100-digit number)
15395985242586213166…54880163500175687679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.079 × 10⁹⁹(100-digit number)
30791970485172426332…09760327000351375359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.158 × 10⁹⁹(100-digit number)
61583940970344852664…19520654000702750719
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,649,665 XPM·at block #6,800,699 · updates every 60s
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