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Block #1,534,420

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 5:35:01 AM Β· Difficulty 10.6179 Β· 5,271,414 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
54036735efbc9d55766dc08541a008a2ae04564eabe640afc4230c1beebce2e3
View on Chainz β†—

Height

#1,534,420

Difficulty

10.617912

Transactions

3

Size

15.01 KB

Version

2

Bits

0a9e2f81

Nonce

1,387,790,774

Timestamp

4/10/2016, 5:35:01 AM

Confirmations

5,271,414

Mined by

⛏️ P2SHAQyFa9dCSkZXhGW5frAmQ8aRXQ7E9wc17m

Merkle Root

3a3b45575dc0d7f6e546b32334f1fc07a6fa1e03571f771027680ae56e60b727
Transactions (3)
Coinbase6c63265e114dc5…62b4ace297ef76
1 in β†’ 1 out9.0200 XPM109 B
AQyFa9dC…7E9wc17m
0cc43bea92f6d1…8112b8386b2af6
51 in β†’ 1 out1108.8822 XPM7.41 KB
AM6J4tAU…Y5vUgH1x
59171d788d231d…ffc066ef4fa7e5
51 in β†’ 1 out2739.4561 XPM7.40 KB
AVKGjowL…QDKXY9D4
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.

2.859 Γ— 10⁹⁡(96-digit number)
28598717345814664493…94070284270097136001
Discovered Prime Numbers
p_k = 2^k Γ— 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
2.859 Γ— 10⁹⁡(96-digit number)
28598717345814664493…94070284270097136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.719 Γ— 10⁹⁡(96-digit number)
57197434691629328987…88140568540194272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.143 Γ— 10⁹⁢(97-digit number)
11439486938325865797…76281137080388544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.287 Γ— 10⁹⁢(97-digit number)
22878973876651731594…52562274160777088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.575 Γ— 10⁹⁢(97-digit number)
45757947753303463189…05124548321554176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.151 Γ— 10⁹⁢(97-digit number)
91515895506606926379…10249096643108352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.830 Γ— 10⁹⁷(98-digit number)
18303179101321385275…20498193286216704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.660 Γ— 10⁹⁷(98-digit number)
36606358202642770551…40996386572433408001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.321 Γ— 10⁹⁷(98-digit number)
73212716405285541103…81992773144866816001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.464 Γ— 10⁹⁸(99-digit number)
14642543281057108220…63985546289733632001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,690,757 XPMΒ·at block #6,805,833 Β· updates every 60s
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