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Block #2,812,954

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2018, 11:44:55 PM Β· Difficulty 11.6747 Β· 4,012,360 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5146cc8028a8c0ffc96f7e504eb8a78843556a65c251433b9ec7be81d1061138
View on Chainz β†—

Height

#2,812,954

Difficulty

11.674723

Transactions

2

Size

1019 B

Version

2

Bits

0bacbaa3

Nonce

70,417,027

Timestamp

8/27/2018, 11:44:55 PM

Confirmations

4,012,360

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

c16ef82c6ccd1415143994c30f0a8c859af84974ee013f5ca7a453ca8c9aff2d
Transactions (2)
Coinbasebb1083dccd37a0…e5d55bac47725e
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
d1b8fd6da7b0f5…cbd5387f8e8017
5 in β†’ 2 out5603.7932 XPM819 B
AUaHxvoV…eXzf2RPSAMRycWoF…13hkF5ou
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.

1.240 Γ— 10⁹⁡(96-digit number)
12403486370639775252…59358262884167305601
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
1.240 Γ— 10⁹⁡(96-digit number)
12403486370639775252…59358262884167305601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.480 Γ— 10⁹⁡(96-digit number)
24806972741279550504…18716525768334611201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.961 Γ— 10⁹⁡(96-digit number)
49613945482559101008…37433051536669222401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.922 Γ— 10⁹⁡(96-digit number)
99227890965118202016…74866103073338444801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.984 Γ— 10⁹⁢(97-digit number)
19845578193023640403…49732206146676889601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.969 Γ— 10⁹⁢(97-digit number)
39691156386047280806…99464412293353779201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.938 Γ— 10⁹⁢(97-digit number)
79382312772094561612…98928824586707558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.587 Γ— 10⁹⁷(98-digit number)
15876462554418912322…97857649173415116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.175 Γ— 10⁹⁷(98-digit number)
31752925108837824645…95715298346830233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.350 Γ— 10⁹⁷(98-digit number)
63505850217675649290…91430596693660467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.270 Γ— 10⁹⁸(99-digit number)
12701170043535129858…82861193387320934401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,846,615 XPMΒ·at block #6,825,313 Β· updates every 60s
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