Block #1,348,977

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/30/2015, 7:07:32 PM · Difficulty 10.8154 · 5,476,324 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
78e3284e79bf25cf5c08209f94791df6ff49c94f2189fac2dafa85d3032ade2f

Height

#1,348,977

Difficulty

10.815432

Transactions

2

Size

1.15 KB

Version

2

Bits

0ad0c02d

Nonce

1,190,801,110

Timestamp

11/30/2015, 7:07:32 PM

Confirmations

5,476,324

Merkle Root

fe42cae5d0c55634298561f154277db58b6897477ca9c9ca970ad3c85a70c523
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.

9.543 × 10⁹³(94-digit number)
95430478257432943033…67984611701015500599
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
9.543 × 10⁹³(94-digit number)
95430478257432943033…67984611701015500599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.908 × 10⁹⁴(95-digit number)
19086095651486588606…35969223402031001199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.817 × 10⁹⁴(95-digit number)
38172191302973177213…71938446804062002399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.634 × 10⁹⁴(95-digit number)
76344382605946354426…43876893608124004799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.526 × 10⁹⁵(96-digit number)
15268876521189270885…87753787216248009599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.053 × 10⁹⁵(96-digit number)
30537753042378541770…75507574432496019199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.107 × 10⁹⁵(96-digit number)
61075506084757083541…51015148864992038399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.221 × 10⁹⁶(97-digit number)
12215101216951416708…02030297729984076799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.443 × 10⁹⁶(97-digit number)
24430202433902833416…04060595459968153599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.886 × 10⁹⁶(97-digit number)
48860404867805666833…08121190919936307199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
9.772 × 10⁹⁶(97-digit number)
97720809735611333666…16242381839872614399
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:57,846,509 XPM·at block #6,825,300 · updates every 60s
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