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Block #576,515

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2014, 3:40:58 PM Β· Difficulty 10.9689 Β· 6,250,247 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0bf1665b211f77228074bbd33e5ef15a2199e99ae00cdd26a2ae1f52adcf2da7
View on Chainz β†—

Height

#576,515

Difficulty

10.968852

Transactions

1

Size

208 B

Version

2

Bits

0af806a7

Nonce

490,615,620

Timestamp

6/4/2014, 3:40:58 PM

Confirmations

6,250,247

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

24635984a6f782111aef70d549d2ce2c600f01aa174443b8c64f6cf90719d992
Transactions (1)
Coinbase24635984a6f782…4f6cf90719d992
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

9.441 Γ— 10⁹⁹(100-digit number)
94410452612151291241…41203957110638540801
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
9.441 Γ— 10⁹⁹(100-digit number)
94410452612151291241…41203957110638540801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.888 Γ— 10¹⁰⁰(101-digit number)
18882090522430258248…82407914221277081601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.776 Γ— 10¹⁰⁰(101-digit number)
37764181044860516496…64815828442554163201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.552 Γ— 10¹⁰⁰(101-digit number)
75528362089721032993…29631656885108326401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.510 Γ— 10¹⁰¹(102-digit number)
15105672417944206598…59263313770216652801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.021 Γ— 10¹⁰¹(102-digit number)
30211344835888413197…18526627540433305601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.042 Γ— 10¹⁰¹(102-digit number)
60422689671776826394…37053255080866611201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.208 Γ— 10¹⁰²(103-digit number)
12084537934355365278…74106510161733222401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.416 Γ— 10¹⁰²(103-digit number)
24169075868710730557…48213020323466444801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.833 Γ— 10¹⁰²(103-digit number)
48338151737421461115…96426040646932889601
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:57,858,255 XPMΒ·at block #6,826,761 Β· updates every 60s
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