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Block #1,029,910

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/23/2015, 9:01:19 PM Β· Difficulty 10.7598 Β· 5,797,245 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5798875853ac297d3428a9f1ae4e46e3f9aa38235e93f02da1ab873b21535363
View on Chainz β†—

Height

#1,029,910

Difficulty

10.759812

Transactions

2

Size

614 B

Version

2

Bits

0ac2830a

Nonce

118,977,086

Timestamp

4/23/2015, 9:01:19 PM

Confirmations

5,797,245

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

706ca6310b434f67e564185665e77bbe39e7daf4387c48a2735aa8d0bb56bdf2
Transactions (2)
Coinbase1127d760e2ea3c…a51864ce50af1c
1 in β†’ 1 out8.6300 XPM116 B
ANSXnLY2…Sd25TjkD
622788c8bd08e4…c03364c0fd0b03
2 in β†’ 3 out1.2762 XPM407 B
AKsebF9o…26T4a6vnAR7jw5dC…9Fcf7U67AR6qgsuL…x1tjMz93
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.

2.279 Γ— 10⁹⁢(97-digit number)
22791373770354356137…74056481031722160641
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
2.279 Γ— 10⁹⁢(97-digit number)
22791373770354356137…74056481031722160641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.558 Γ— 10⁹⁢(97-digit number)
45582747540708712274…48112962063444321281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.116 Γ— 10⁹⁢(97-digit number)
91165495081417424549…96225924126888642561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.823 Γ— 10⁹⁷(98-digit number)
18233099016283484909…92451848253777285121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.646 Γ— 10⁹⁷(98-digit number)
36466198032566969819…84903696507554570241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.293 Γ— 10⁹⁷(98-digit number)
72932396065133939639…69807393015109140481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.458 Γ— 10⁹⁸(99-digit number)
14586479213026787927…39614786030218280961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.917 Γ— 10⁹⁸(99-digit number)
29172958426053575855…79229572060436561921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.834 Γ— 10⁹⁸(99-digit number)
58345916852107151711…58459144120873123841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.166 Γ— 10⁹⁹(100-digit number)
11669183370421430342…16918288241746247681
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:57,861,424 XPMΒ·at block #6,827,154 Β· updates every 60s
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