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Block #1,693,746

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/29/2016, 8:05:49 AM Β· Difficulty 10.6786 Β· 5,120,636 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2e1240e9a6ad0b6d3ca965e88c60c5a9fd73585f76c8717c66234413a0597b8d
View on Chainz β†—

Height

#1,693,746

Difficulty

10.678573

Transactions

2

Size

1.14 KB

Version

2

Bits

0aadb6f9

Nonce

980,911,900

Timestamp

7/29/2016, 8:05:49 AM

Confirmations

5,120,636

Mined by

⛏️ P2SHAcBi8DeADucUKEPkbVLgaMaDXnkaLsjcNp

Merkle Root

014c467be9fd3d686fefe12cb45cd3db083f4205fcb7a3545098ed844af46d8c
Transactions (2)
Coinbasefe463e05670863…238e5e02fb06c6
1 in β†’ 1 out8.7700 XPM110 B
AcBi8DeA…kaLsjcNp
93ae81d6761e84…4e47edb9f1b18f
6 in β†’ 2 out449.0000 XPM970 B
AcDhjHA9…ebukETHzALz3G89o…Wkd7apD1
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.

3.009 Γ— 10⁹⁴(95-digit number)
30090965195270318316…95513692564259695199
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.009 Γ— 10⁹⁴(95-digit number)
30090965195270318316…95513692564259695199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.018 Γ— 10⁹⁴(95-digit number)
60181930390540636633…91027385128519390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁡(96-digit number)
12036386078108127326…82054770257038780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.407 Γ— 10⁹⁡(96-digit number)
24072772156216254653…64109540514077561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.814 Γ— 10⁹⁡(96-digit number)
48145544312432509306…28219081028155123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.629 Γ— 10⁹⁡(96-digit number)
96291088624865018613…56438162056310246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.925 Γ— 10⁹⁢(97-digit number)
19258217724973003722…12876324112620492799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.851 Γ— 10⁹⁢(97-digit number)
38516435449946007445…25752648225240985599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.703 Γ— 10⁹⁢(97-digit number)
77032870899892014890…51505296450481971199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.540 Γ— 10⁹⁷(98-digit number)
15406574179978402978…03010592900963942399
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,759,116 XPMΒ·at block #6,814,381 Β· updates every 60s
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