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Block #2,108,333

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/9/2017, 12:30:52 PM Β· Difficulty 10.8969 Β· 4,733,570 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c9b1eb16fa182aee55d8badfd7f03ad56b360b28b046fd4ebe39609903578da3
View on Chainz β†—

Height

#2,108,333

Difficulty

10.896889

Transactions

2

Size

392 B

Version

2

Bits

0ae59a86

Nonce

238,503,018

Timestamp

5/9/2017, 12:30:52 PM

Confirmations

4,733,570

Mined by

⛏️ P2SHAPNPGQA4Fyf3g5MPukczTHkV3NuKzYNtug

Merkle Root

d5ab3993556e768b8346112c4b73aeb62bc36bfa6dbefbaf2c96674cd6ed6f2d
Transactions (2)
Coinbased51ef04a362a8a…a2cb1f755d781a
1 in β†’ 1 out8.4200 XPM110 B
APNPGQA4…uKzYNtug
408e0900725eb2…2fe8ec656a855c
1 in β†’ 1 out0.1151 XPM192 B
AaV6QwHy…ZqrytAax
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.

1.003 Γ— 10⁹⁡(96-digit number)
10038900500138389832…00407202006331658239
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
1.003 Γ— 10⁹⁡(96-digit number)
10038900500138389832…00407202006331658239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.007 Γ— 10⁹⁡(96-digit number)
20077801000276779664…00814404012663316479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.015 Γ— 10⁹⁡(96-digit number)
40155602000553559328…01628808025326632959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.031 Γ— 10⁹⁡(96-digit number)
80311204001107118657…03257616050653265919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.606 Γ— 10⁹⁢(97-digit number)
16062240800221423731…06515232101306531839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.212 Γ— 10⁹⁢(97-digit number)
32124481600442847462…13030464202613063679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.424 Γ— 10⁹⁢(97-digit number)
64248963200885694925…26060928405226127359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.284 Γ— 10⁹⁷(98-digit number)
12849792640177138985…52121856810452254719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.569 Γ— 10⁹⁷(98-digit number)
25699585280354277970…04243713620904509439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.139 Γ— 10⁹⁷(98-digit number)
51399170560708555940…08487427241809018879
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:57,979,598 XPMΒ·at block #6,841,902 Β· updates every 60s
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