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Block #924,768

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/6/2015, 7:02:14 AM Β· Difficulty 10.9108 Β· 5,884,210 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3ef3426d56e534eae28904a5bfd6e562bcde2b4d650e3b2a40525ae75a744563
View on Chainz β†—

Height

#924,768

Difficulty

10.910790

Transactions

2

Size

539 B

Version

2

Bits

0ae9298d

Nonce

1,808,866,612

Timestamp

2/6/2015, 7:02:14 AM

Confirmations

5,884,210

Mined by

⛏️ P2SHAL3QdVvip5LnAfemkokMHhdPDVhykdsz9y

Merkle Root

4d9904f7b278720d995b8ea5686dec65d89fefe5fc3637f247d3e4838d463599
Transactions (2)
Coinbase67304acc0a20fc…03f673bc9d8a12
1 in β†’ 1 out8.4000 XPM109 B
AL3QdVvi…hykdsz9y
5bd1566a49bca4…47307c75746e3b
2 in β†’ 1 out14.8629 XPM340 B
AWF4rtPp…LnbQHVaN
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.

4.295 Γ— 10⁹⁴(95-digit number)
42954319629763402333…36359661999358238721
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
4.295 Γ— 10⁹⁴(95-digit number)
42954319629763402333…36359661999358238721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.590 Γ— 10⁹⁴(95-digit number)
85908639259526804667…72719323998716477441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.718 Γ— 10⁹⁡(96-digit number)
17181727851905360933…45438647997432954881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.436 Γ— 10⁹⁡(96-digit number)
34363455703810721867…90877295994865909761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.872 Γ— 10⁹⁡(96-digit number)
68726911407621443734…81754591989731819521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.374 Γ— 10⁹⁢(97-digit number)
13745382281524288746…63509183979463639041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.749 Γ— 10⁹⁢(97-digit number)
27490764563048577493…27018367958927278081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.498 Γ— 10⁹⁢(97-digit number)
54981529126097154987…54036735917854556161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.099 Γ— 10⁹⁷(98-digit number)
10996305825219430997…08073471835709112321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.199 Γ— 10⁹⁷(98-digit number)
21992611650438861994…16146943671418224641
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:57,715,880 XPMΒ·at block #6,808,977 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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