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Block #1,429,566

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/26/2016, 11:59:41 PM Β· Difficulty 10.7412 Β· 5,414,377 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
57b6b9d9c8fe7c00c06c2e912456064e3fb4c753eee37830f251c0c1fda339d6
View on Chainz β†—

Height

#1,429,566

Difficulty

10.741163

Transactions

1

Size

201 B

Version

2

Bits

0abdbce2

Nonce

62,349,153

Timestamp

1/26/2016, 11:59:41 PM

Confirmations

5,414,377

Mined by

⛏️ P2SHALdBgM5uwgaX3hEBP5PrKkQsGUSXkcEWGv

Merkle Root

c62b5694abe6ffdd62f863b10741fd1a12bef066dc584ff649904ce4c114cfa0
Transactions (1)
Coinbasec62b5694abe6ff…904ce4c114cfa0
1 in β†’ 1 out8.6500 XPM110 B
ALdBgM5u…SXkcEWGv
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.

9.331 Γ— 10⁹⁡(96-digit number)
93314717706302124586…71412423083458057761
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
9.331 Γ— 10⁹⁡(96-digit number)
93314717706302124586…71412423083458057761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.866 Γ— 10⁹⁢(97-digit number)
18662943541260424917…42824846166916115521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.732 Γ— 10⁹⁢(97-digit number)
37325887082520849834…85649692333832231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.465 Γ— 10⁹⁢(97-digit number)
74651774165041699669…71299384667664462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.493 Γ— 10⁹⁷(98-digit number)
14930354833008339933…42598769335328924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.986 Γ— 10⁹⁷(98-digit number)
29860709666016679867…85197538670657848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.972 Γ— 10⁹⁷(98-digit number)
59721419332033359735…70395077341315696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.194 Γ— 10⁹⁸(99-digit number)
11944283866406671947…40790154682631393281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.388 Γ— 10⁹⁸(99-digit number)
23888567732813343894…81580309365262786561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.777 Γ— 10⁹⁸(99-digit number)
47777135465626687788…63160618730525573121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.555 Γ— 10⁹⁸(99-digit number)
95554270931253375576…26321237461051146241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.911 Γ— 10⁹⁹(100-digit number)
19110854186250675115…52642474922102292481
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,995,919 XPMΒ·at block #6,843,942 Β· updates every 60s
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