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Block #552,242

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2014, 8:31:58 AM Β· Difficulty 10.9627 Β· 6,258,610 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0822c116db57301fe6e3081e74d61335804b8c944d36f411c0a02674e4251c87
View on Chainz β†—

Height

#552,242

Difficulty

10.962658

Transactions

2

Size

692 B

Version

2

Bits

0af670c2

Nonce

77,741,507

Timestamp

5/19/2014, 8:31:58 AM

Confirmations

6,258,610

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d7a97f9b2e9940b8d655db307c5e4d8c83c412078404845c0dc2204c6d43493b
Transactions (2)
Coinbase0e4a07eba2a743…7afe565070fb37
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
a6f5d44e1fca1c…01c6d2ca588e34
3 in β†’ 1 out0.9935 XPM485 B
AMPRMjEE…DrNwu4Bp
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.

5.656 Γ— 10⁹⁷(98-digit number)
56563134539442412172…01016034629266734941
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
5.656 Γ— 10⁹⁷(98-digit number)
56563134539442412172…01016034629266734941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.131 Γ— 10⁹⁸(99-digit number)
11312626907888482434…02032069258533469881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.262 Γ— 10⁹⁸(99-digit number)
22625253815776964869…04064138517066939761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.525 Γ— 10⁹⁸(99-digit number)
45250507631553929738…08128277034133879521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.050 Γ— 10⁹⁸(99-digit number)
90501015263107859476…16256554068267759041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.810 Γ— 10⁹⁹(100-digit number)
18100203052621571895…32513108136535518081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.620 Γ— 10⁹⁹(100-digit number)
36200406105243143790…65026216273071036161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.240 Γ— 10⁹⁹(100-digit number)
72400812210486287581…30052432546142072321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.448 Γ— 10¹⁰⁰(101-digit number)
14480162442097257516…60104865092284144641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.896 Γ— 10¹⁰⁰(101-digit number)
28960324884194515032…20209730184568289281
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:57,730,912 XPMΒ·at block #6,810,851 Β· updates every 60s
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