Block #1,238,497

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/15/2015, 11:02:04 PM · Difficulty 10.7571 · 5,578,049 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0972e3f3fe131c7cf39c300b62db39c8ac01a13586425484255550845de78362

Height

#1,238,497

Difficulty

10.757071

Transactions

2

Size

874 B

Version

2

Bits

0ac1cf65

Nonce

25,321,103

Timestamp

9/15/2015, 11:02:04 PM

Confirmations

5,578,049

Merkle Root

64c8c37dd4de079fb5a0f3f20ee17a0b5fc05a2668323811b07b4c507b3736b8
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.

8.151 × 10⁹⁵(96-digit number)
81517421079959326464…31258018588352957439
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
8.151 × 10⁹⁵(96-digit number)
81517421079959326464…31258018588352957439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.630 × 10⁹⁶(97-digit number)
16303484215991865292…62516037176705914879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.260 × 10⁹⁶(97-digit number)
32606968431983730585…25032074353411829759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.521 × 10⁹⁶(97-digit number)
65213936863967461171…50064148706823659519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.304 × 10⁹⁷(98-digit number)
13042787372793492234…00128297413647319039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.608 × 10⁹⁷(98-digit number)
26085574745586984468…00256594827294638079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.217 × 10⁹⁷(98-digit number)
52171149491173968937…00513189654589276159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.043 × 10⁹⁸(99-digit number)
10434229898234793787…01026379309178552319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.086 × 10⁹⁸(99-digit number)
20868459796469587575…02052758618357104639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.173 × 10⁹⁸(99-digit number)
41736919592939175150…04105517236714209279
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:57,776,497 XPM·at block #6,816,545 · updates every 60s
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