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Block #547,821

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2014, 4:45:37 PM Β· Difficulty 10.9578 Β· 6,248,291 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
31ca097db5d722769087d40efab9abd21382997ef9ff411d2513bd2a1d56de84
View on Chainz β†—

Height

#547,821

Difficulty

10.957827

Transactions

2

Size

434 B

Version

2

Bits

0af53428

Nonce

386,908,426

Timestamp

5/16/2014, 4:45:37 PM

Confirmations

6,248,291

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

40081e5f75c7d6bd7e7655c5eb1dd89c0eace742e871632f5f169d5840cc5635
Transactions (2)
Coinbasef8686128e74c1c…060fd223837301
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
5b91d9c4c7fb11…4124f2480cda8e
1 in β†’ 3 out8.3200 XPM227 B
AeKNrjNj…1NEq95TaAVrD6maY…W77cdqzzAeqZw9yo…5K9AMCop
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.

1.567 Γ— 10⁹⁸(99-digit number)
15675820618929336831…95789114983062341501
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
1.567 Γ— 10⁹⁸(99-digit number)
15675820618929336831…95789114983062341501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.135 Γ— 10⁹⁸(99-digit number)
31351641237858673663…91578229966124683001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.270 Γ— 10⁹⁸(99-digit number)
62703282475717347326…83156459932249366001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.254 Γ— 10⁹⁹(100-digit number)
12540656495143469465…66312919864498732001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.508 Γ— 10⁹⁹(100-digit number)
25081312990286938930…32625839728997464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.016 Γ— 10⁹⁹(100-digit number)
50162625980573877861…65251679457994928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.003 Γ— 10¹⁰⁰(101-digit number)
10032525196114775572…30503358915989856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.006 Γ— 10¹⁰⁰(101-digit number)
20065050392229551144…61006717831979712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.013 Γ— 10¹⁰⁰(101-digit number)
40130100784459102289…22013435663959424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.026 Γ— 10¹⁰⁰(101-digit number)
80260201568918204578…44026871327918848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.605 Γ— 10¹⁰¹(102-digit number)
16052040313783640915…88053742655837696001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,612,891 XPMΒ·at block #6,796,111 Β· updates every 60s
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