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Block #1,534,425

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 5:39:30 AM Β· Difficulty 10.6177 Β· 5,282,209 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
38e62bed65c7d493543f23b31498017c9b5a55fd7948c669e5f1543297856bb8
View on Chainz β†—

Height

#1,534,425

Difficulty

10.617742

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e2455

Nonce

2,128,211,055

Timestamp

4/10/2016, 5:39:30 AM

Confirmations

5,282,209

Mined by

⛏️ P2SHAbxbP7tLtBymYucqz78scHMRPTGEU7GwXs

Merkle Root

8a2d8d0000120e71b896d31503c3636dd6e19ccfa41127070b9239dada744d81
Transactions (2)
Coinbase6a24b8a29007eb…4543eb9b475e48
1 in β†’ 1 out8.9400 XPM110 B
AbxbP7tL…GEU7GwXs
0e96cf715358c5…5ab0a08cf62a15
51 in β†’ 1 out2745.7750 XPM7.41 KB
APQWGTCU…2TovK3Cp
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.

1.196 Γ— 10⁹⁢(97-digit number)
11966763757946640431…76143178865057464321
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
1.196 Γ— 10⁹⁢(97-digit number)
11966763757946640431…76143178865057464321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.393 Γ— 10⁹⁢(97-digit number)
23933527515893280862…52286357730114928641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.786 Γ— 10⁹⁢(97-digit number)
47867055031786561725…04572715460229857281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.573 Γ— 10⁹⁢(97-digit number)
95734110063573123450…09145430920459714561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.914 Γ— 10⁹⁷(98-digit number)
19146822012714624690…18290861840919429121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.829 Γ— 10⁹⁷(98-digit number)
38293644025429249380…36581723681838858241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.658 Γ— 10⁹⁷(98-digit number)
76587288050858498760…73163447363677716481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.531 Γ— 10⁹⁸(99-digit number)
15317457610171699752…46326894727355432961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.063 Γ— 10⁹⁸(99-digit number)
30634915220343399504…92653789454710865921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.126 Γ— 10⁹⁸(99-digit number)
61269830440686799008…85307578909421731841
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:57,777,187 XPMΒ·at block #6,816,633 Β· updates every 60s
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