Block #1,497,422

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/15/2016, 6:10:19 AM · Difficulty 10.6456 · 5,335,975 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0e3b648eb57d0c7417e25a032695dee0a4d1bb69a3b319603085823fbd81cab8

Height

#1,497,422

Difficulty

10.645586

Transactions

2

Size

1003 B

Version

2

Bits

0aa5451b

Nonce

520,316,736

Timestamp

3/15/2016, 6:10:19 AM

Confirmations

5,335,975

Merkle Root

71b06efcf54f49b54c04c6c01f0d1ee55df69a09a4e9ce6b65a0b0bf55b1f620
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.

1.236 × 10⁹⁵(96-digit number)
12361031332737598080…23497971238729501439
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
1.236 × 10⁹⁵(96-digit number)
12361031332737598080…23497971238729501439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.472 × 10⁹⁵(96-digit number)
24722062665475196160…46995942477459002879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.944 × 10⁹⁵(96-digit number)
49444125330950392321…93991884954918005759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.888 × 10⁹⁵(96-digit number)
98888250661900784643…87983769909836011519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.977 × 10⁹⁶(97-digit number)
19777650132380156928…75967539819672023039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.955 × 10⁹⁶(97-digit number)
39555300264760313857…51935079639344046079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.911 × 10⁹⁶(97-digit number)
79110600529520627715…03870159278688092159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.582 × 10⁹⁷(98-digit number)
15822120105904125543…07740318557376184319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.164 × 10⁹⁷(98-digit number)
31644240211808251086…15480637114752368639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.328 × 10⁹⁷(98-digit number)
63288480423616502172…30961274229504737279
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:57,911,376 XPM·at block #6,833,396 · updates every 60s
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