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Block #2,456,995

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 1/4/2018, 8:56:31 AM Β· Difficulty 10.9537 Β· 4,385,140 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
28aa1c8c203ebf95ebf0b20298abfa2d1e2f47d41a7ea2c1ee2b8e69c45e5c53
View on Chainz β†—

Height

#2,456,995

Difficulty

10.953709

Transactions

2

Size

722 B

Version

2

Bits

0af42647

Nonce

680,684,131

Timestamp

1/4/2018, 8:56:31 AM

Confirmations

4,385,140

Mined by

⛏️ P2SHAQEp5Wc3xhGvgNGKQTMuqoDBnCtPd9hSww

Merkle Root

9d9c5dcb99cf73a53adca6c0678cbda20e06390f53fd367c0ce7b80b901c5438
Transactions (2)
Coinbasefac1e980621062…9cde20d4c1c1ea
1 in β†’ 1 out8.3300 XPM109 B
AQEp5Wc3…tPd9hSww
a6b2393c352952…14772296ac81a9
3 in β†’ 2 out1.0105 XPM524 B
AJCtPzZC…PvtFWS9nAH5jcgi4…6HZ7vbiD
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.

1.457 Γ— 10⁹²(93-digit number)
14573252580402738471…12061140447387648359
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
1.457 Γ— 10⁹²(93-digit number)
14573252580402738471…12061140447387648359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.914 Γ— 10⁹²(93-digit number)
29146505160805476942…24122280894775296719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.829 Γ— 10⁹²(93-digit number)
58293010321610953885…48244561789550593439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.165 Γ— 10⁹³(94-digit number)
11658602064322190777…96489123579101186879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.331 Γ— 10⁹³(94-digit number)
23317204128644381554…92978247158202373759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.663 Γ— 10⁹³(94-digit number)
46634408257288763108…85956494316404747519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.326 Γ— 10⁹³(94-digit number)
93268816514577526216…71912988632809495039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.865 Γ— 10⁹⁴(95-digit number)
18653763302915505243…43825977265618990079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.730 Γ— 10⁹⁴(95-digit number)
37307526605831010486…87651954531237980159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.461 Γ— 10⁹⁴(95-digit number)
74615053211662020973…75303909062475960319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁡(96-digit number)
14923010642332404194…50607818124951920639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.984 Γ— 10⁹⁡(96-digit number)
29846021284664808389…01215636249903841279
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,981,470 XPMΒ·at block #6,842,134 Β· updates every 60s
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