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Block #1,534,791

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 11:38:47 AM Β· Difficulty 10.6181 Β· 5,274,685 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
38879a8b1fd487a1576e18d0275523e68560a7d705ccf6bf113e4936c6bac056
View on Chainz β†—

Height

#1,534,791

Difficulty

10.618100

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e3bd2

Nonce

130,337,037

Timestamp

4/10/2016, 11:38:47 AM

Confirmations

5,274,685

Mined by

⛏️ P2SHAXLqUUZZFSpAhGAmU45ShyJgfesADp5BH5

Merkle Root

b424cbb917381ecd9a06f84c924f08e4fe16204e1d4e14d9563e2c8e6f57ac45
Transactions (2)
Coinbase75ccdd7363643c…ecc845c174a464
1 in β†’ 1 out8.9400 XPM109 B
AXLqUUZZ…sADp5BH5
035049cfe808f7…47b8aca27d53e7
51 in β†’ 1 out3188.4065 XPM7.41 KB
ANuGBFjo…5bEyHLtn
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.

1.020 Γ— 10⁹⁡(96-digit number)
10203397077299570853…17903794675741964159
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
1.020 Γ— 10⁹⁡(96-digit number)
10203397077299570853…17903794675741964159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.040 Γ— 10⁹⁡(96-digit number)
20406794154599141707…35807589351483928319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.081 Γ— 10⁹⁡(96-digit number)
40813588309198283415…71615178702967856639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.162 Γ— 10⁹⁡(96-digit number)
81627176618396566831…43230357405935713279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.632 Γ— 10⁹⁢(97-digit number)
16325435323679313366…86460714811871426559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.265 Γ— 10⁹⁢(97-digit number)
32650870647358626732…72921429623742853119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.530 Γ— 10⁹⁢(97-digit number)
65301741294717253464…45842859247485706239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.306 Γ— 10⁹⁷(98-digit number)
13060348258943450692…91685718494971412479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.612 Γ— 10⁹⁷(98-digit number)
26120696517886901385…83371436989942824959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.224 Γ— 10⁹⁷(98-digit number)
52241393035773802771…66742873979885649919
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:57,719,880 XPMΒ·at block #6,809,475 Β· updates every 60s
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