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Block #1,597,717

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/24/2016, 7:04:33 AM Β· Difficulty 10.6090 Β· 5,229,124 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
00dfa88a66bdf379809441895427b0767d39bf08ec99c6be2bafc6d059d102b4
View on Chainz β†—

Height

#1,597,717

Difficulty

10.609045

Transactions

1

Size

201 B

Version

2

Bits

0a9bea5c

Nonce

1,698,647,866

Timestamp

5/24/2016, 7:04:33 AM

Confirmations

5,229,124

Mined by

⛏️ P2SHAeWZpRnP34A4GJ8rXXuHLer3mSs39QQo5k

Merkle Root

a9f05290d1661eafc48c47f64724f0cda23c013ebc016383880b467169edea5b
Transactions (1)
Coinbasea9f05290d1661e…0b467169edea5b
1 in β†’ 1 out8.8700 XPM110 B
AeWZpRnP…s39QQo5k
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.510 Γ— 10⁹⁡(96-digit number)
65101857021563742510…40325816812358712319
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.510 Γ— 10⁹⁡(96-digit number)
65101857021563742510…40325816812358712319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.302 Γ— 10⁹⁢(97-digit number)
13020371404312748502…80651633624717424639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.604 Γ— 10⁹⁢(97-digit number)
26040742808625497004…61303267249434849279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.208 Γ— 10⁹⁢(97-digit number)
52081485617250994008…22606534498869698559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.041 Γ— 10⁹⁷(98-digit number)
10416297123450198801…45213068997739397119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.083 Γ— 10⁹⁷(98-digit number)
20832594246900397603…90426137995478794239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.166 Γ— 10⁹⁷(98-digit number)
41665188493800795206…80852275990957588479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.333 Γ— 10⁹⁷(98-digit number)
83330376987601590413…61704551981915176959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.666 Γ— 10⁹⁸(99-digit number)
16666075397520318082…23409103963830353919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.333 Γ— 10⁹⁸(99-digit number)
33332150795040636165…46818207927660707839
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,858,893 XPMΒ·at block #6,826,840 Β· updates every 60s
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