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Block #544,292

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/14/2014, 7:42:33 PM Β· Difficulty 10.9502 Β· 6,251,857 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
35da19cc062800a54bcd43111f13743eb36fa8ea93e403e16cc7f3419bdd0c91
View on Chainz β†—

Height

#544,292

Difficulty

10.950198

Transactions

2

Size

2.12 KB

Version

2

Bits

0af3402a

Nonce

718,171,877

Timestamp

5/14/2014, 7:42:33 PM

Confirmations

6,251,857

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5631cf43fa8b7b4f8e0369761d62ba50924a7e75f78c32315503f3462d75ffc5
Transactions (2)
Coinbasef1f266c90a036c…e23d5bb1ea9416
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
f3b81424773f15…3aafe38ea3c9b0
13 in β†’ 1 out39.0408 XPM1.92 KB
AYfGXBG3…s4uNnsy3
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.

5.759 Γ— 10⁹⁷(98-digit number)
57591853782339390804…34443821185247920001
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
5.759 Γ— 10⁹⁷(98-digit number)
57591853782339390804…34443821185247920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.151 Γ— 10⁹⁸(99-digit number)
11518370756467878160…68887642370495840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.303 Γ— 10⁹⁸(99-digit number)
23036741512935756321…37775284740991680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.607 Γ— 10⁹⁸(99-digit number)
46073483025871512643…75550569481983360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.214 Γ— 10⁹⁸(99-digit number)
92146966051743025287…51101138963966720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.842 Γ— 10⁹⁹(100-digit number)
18429393210348605057…02202277927933440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.685 Γ— 10⁹⁹(100-digit number)
36858786420697210115…04404555855866880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.371 Γ— 10⁹⁹(100-digit number)
73717572841394420230…08809111711733760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.474 Γ— 10¹⁰⁰(101-digit number)
14743514568278884046…17618223423467520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.948 Γ— 10¹⁰⁰(101-digit number)
29487029136557768092…35236446846935040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.897 Γ— 10¹⁰⁰(101-digit number)
58974058273115536184…70472893693870080001
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:57,613,190 XPMΒ·at block #6,796,148 Β· updates every 60s
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