Block #2,173,078

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/23/2017, 2:27:16 AM · Difficulty 10.9095 · 4,668,751 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8fcebf4912c4b65e9c8063debdfb76c1d0e846a2a55864d9aac82274666df8b5

Height

#2,173,078

Difficulty

10.909522

Transactions

4

Size

1.44 KB

Version

2

Bits

0ae8d670

Nonce

677,440,871

Timestamp

6/23/2017, 2:27:16 AM

Confirmations

4,668,751

Merkle Root

90c636cc17b5e1e71f1eb6585053358244e4ece4e7208b9222c9ec2b6c3843eb
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.

2.312 × 10⁹⁴(95-digit number)
23127975714983734628…71725076745198035999
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
2.312 × 10⁹⁴(95-digit number)
23127975714983734628…71725076745198035999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.625 × 10⁹⁴(95-digit number)
46255951429967469257…43450153490396071999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.251 × 10⁹⁴(95-digit number)
92511902859934938515…86900306980792143999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.850 × 10⁹⁵(96-digit number)
18502380571986987703…73800613961584287999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.700 × 10⁹⁵(96-digit number)
37004761143973975406…47601227923168575999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.400 × 10⁹⁵(96-digit number)
74009522287947950812…95202455846337151999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.480 × 10⁹⁶(97-digit number)
14801904457589590162…90404911692674303999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.960 × 10⁹⁶(97-digit number)
29603808915179180324…80809823385348607999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.920 × 10⁹⁶(97-digit number)
59207617830358360649…61619646770697215999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.184 × 10⁹⁷(98-digit number)
11841523566071672129…23239293541394431999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.368 × 10⁹⁷(98-digit number)
23683047132143344259…46478587082788863999
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,979,005 XPM·at block #6,841,828 · updates every 60s
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