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Block #1,496,749

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/14/2016, 7:21:51 PM Β· Difficulty 10.6439 Β· 5,298,871 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
61089dc6d979a0c310cd02b84601f39dcc43a382d613918ca99a3e56b4a3541b
View on Chainz β†—

Height

#1,496,749

Difficulty

10.643930

Transactions

2

Size

1.97 KB

Version

2

Bits

0aa4d89a

Nonce

20,121,968

Timestamp

3/14/2016, 7:21:51 PM

Confirmations

5,298,871

Mined by

⛏️ P2SHAPzB6LQGFFmNSJDZN1kFyqbhZQ68a1J568

Merkle Root

a28afe8b2be15d4c850a54f52de7e11b1867f13637c9c0be1a0410260fa5c2a9
Transactions (2)
Coinbase2e0ce1f2d75ae7…d8881b01384ae7
1 in β†’ 1 out8.8300 XPM109 B
APzB6LQG…68a1J568
69bc128b0c4187…926cd5048d1439
12 in β†’ 1 out35.3542 XPM1.78 KB
AbED3Tup…iyc2HscG
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.

8.771 Γ— 10⁹¹(92-digit number)
87711929348894330274…42476836080729138619
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
8.771 Γ— 10⁹¹(92-digit number)
87711929348894330274…42476836080729138619
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.754 Γ— 10⁹²(93-digit number)
17542385869778866054…84953672161458277239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.508 Γ— 10⁹²(93-digit number)
35084771739557732109…69907344322916554479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.016 Γ— 10⁹²(93-digit number)
70169543479115464219…39814688645833108959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.403 Γ— 10⁹³(94-digit number)
14033908695823092843…79629377291666217919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.806 Γ— 10⁹³(94-digit number)
28067817391646185687…59258754583332435839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.613 Γ— 10⁹³(94-digit number)
56135634783292371375…18517509166664871679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.122 Γ— 10⁹⁴(95-digit number)
11227126956658474275…37035018333329743359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.245 Γ— 10⁹⁴(95-digit number)
22454253913316948550…74070036666659486719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.490 Γ— 10⁹⁴(95-digit number)
44908507826633897100…48140073333318973439
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:57,609,026 XPMΒ·at block #6,795,619 Β· updates every 60s
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