Block #1,184,429

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 8/6/2015, 8:26:41 AM · Difficulty 10.8978 · 5,621,788 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d7dedec16f78367cb84cb1dedb949a4f453e415e49c8610ed6ca2a99f7294a78

Height

#1,184,429

Difficulty

10.897783

Transactions

3

Size

3.96 KB

Version

2

Bits

0ae5d517

Nonce

250,189,265

Timestamp

8/6/2015, 8:26:41 AM

Confirmations

5,621,788

Merkle Root

9c1245569d290d5a8f6daa20f5d196d20fe4f493e63a8ca1dffb09430e8ad02f
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.

3.759 × 10⁹³(94-digit number)
37590475165773271752…47596842949090919679
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
3.759 × 10⁹³(94-digit number)
37590475165773271752…47596842949090919679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.518 × 10⁹³(94-digit number)
75180950331546543505…95193685898181839359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.503 × 10⁹⁴(95-digit number)
15036190066309308701…90387371796363678719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.007 × 10⁹⁴(95-digit number)
30072380132618617402…80774743592727357439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.014 × 10⁹⁴(95-digit number)
60144760265237234804…61549487185454714879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.202 × 10⁹⁵(96-digit number)
12028952053047446960…23098974370909429759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.405 × 10⁹⁵(96-digit number)
24057904106094893921…46197948741818859519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.811 × 10⁹⁵(96-digit number)
48115808212189787843…92395897483637719039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.623 × 10⁹⁵(96-digit number)
96231616424379575686…84791794967275438079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.924 × 10⁹⁶(97-digit number)
19246323284875915137…69583589934550876159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.849 × 10⁹⁶(97-digit number)
38492646569751830274…39167179869101752319
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:57,693,815 XPM·at block #6,806,216 · updates every 60s
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