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Block #1,715,248

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/13/2016, 11:45:54 AM Β· Difficulty 10.6584 Β· 5,116,399 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
59a19bf6643eab62eb88025c918992852c714ff2371c15aa3eb8006016459904
View on Chainz β†—

Height

#1,715,248

Difficulty

10.658361

Transactions

1

Size

242 B

Version

2

Bits

0aa88a5f

Nonce

152,010,108

Timestamp

8/13/2016, 11:45:54 AM

Confirmations

5,116,399

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

c829c87bc0c00f7868eb1daf0434119c301edf4231d9cee22521922300cb7aa6
Transactions (1)
Coinbasec829c87bc0c00f…21922300cb7aa6
1 in β†’ 2 out8.7900 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

7.283 Γ— 10⁹⁴(95-digit number)
72832912499052274410…92210497925814532179
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
7.283 Γ— 10⁹⁴(95-digit number)
72832912499052274410…92210497925814532179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.456 Γ— 10⁹⁡(96-digit number)
14566582499810454882…84420995851629064359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.913 Γ— 10⁹⁡(96-digit number)
29133164999620909764…68841991703258128719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.826 Γ— 10⁹⁡(96-digit number)
58266329999241819528…37683983406516257439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.165 Γ— 10⁹⁢(97-digit number)
11653265999848363905…75367966813032514879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.330 Γ— 10⁹⁢(97-digit number)
23306531999696727811…50735933626065029759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.661 Γ— 10⁹⁢(97-digit number)
46613063999393455622…01471867252130059519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.322 Γ— 10⁹⁢(97-digit number)
93226127998786911245…02943734504260119039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.864 Γ— 10⁹⁷(98-digit number)
18645225599757382249…05887469008520238079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.729 Γ— 10⁹⁷(98-digit number)
37290451199514764498…11774938017040476159
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:57,897,282 XPMΒ·at block #6,831,646 Β· updates every 60s
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