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Block #576,113

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/4/2014, 9:20:50 AM Β· Difficulty 10.9687 Β· 6,238,075 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f57d50723a0261b30c3a08af01d14342b85b5f7d19f12a1de8937c1730e85622
View on Chainz β†—

Height

#576,113

Difficulty

10.968702

Transactions

1

Size

208 B

Version

2

Bits

0af7fcd9

Nonce

846,043,573

Timestamp

6/4/2014, 9:20:50 AM

Confirmations

6,238,075

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0122351f0b93a00225105bbe04e768c43314cbcc1979f595348c9cffc47980ed
Transactions (1)
Coinbase0122351f0b93a0…8c9cffc47980ed
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.

5.004 Γ— 10⁹⁹(100-digit number)
50045103633688758889…98762656391989247999
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
5.004 Γ— 10⁹⁹(100-digit number)
50045103633688758889…98762656391989247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.000 Γ— 10¹⁰⁰(101-digit number)
10009020726737751777…97525312783978495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.001 Γ— 10¹⁰⁰(101-digit number)
20018041453475503555…95050625567956991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.003 Γ— 10¹⁰⁰(101-digit number)
40036082906951007111…90101251135913983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.007 Γ— 10¹⁰⁰(101-digit number)
80072165813902014223…80202502271827967999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.601 Γ— 10¹⁰¹(102-digit number)
16014433162780402844…60405004543655935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.202 Γ— 10¹⁰¹(102-digit number)
32028866325560805689…20810009087311871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.405 Γ— 10¹⁰¹(102-digit number)
64057732651121611378…41620018174623743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.281 Γ— 10¹⁰²(103-digit number)
12811546530224322275…83240036349247487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.562 Γ— 10¹⁰²(103-digit number)
25623093060448644551…66480072698494975999
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:57,757,577 XPMΒ·at block #6,814,187 Β· updates every 60s
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