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Block #2,856,869

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/27/2018, 8:08:02 AM Β· Difficulty 11.6897 Β· 3,986,548 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2acd73aa78fc292fec2481b8745ca5f803066d870ca2c9aed2b8768aa03a4ff3
View on Chainz β†—

Height

#2,856,869

Difficulty

11.689739

Transactions

1

Size

200 B

Version

2

Bits

0bb092bc

Nonce

1,334,316,569

Timestamp

9/27/2018, 8:08:02 AM

Confirmations

3,986,548

Mined by

⛏️ P2SHALgLQK8Vjd2fjbTB9kra2KnLiZHVC8qvZo

Merkle Root

c6b50271da3b27078e6f0dfe511d56df7b633d04edf87d95ed6d81670994bcc9
Transactions (1)
Coinbasec6b50271da3b27…6d81670994bcc9
1 in β†’ 1 out7.3100 XPM110 B
ALgLQK8V…HVC8qvZo
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.

8.411 Γ— 10⁹⁴(95-digit number)
84112055710520467091…33835509977519710601
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
8.411 Γ— 10⁹⁴(95-digit number)
84112055710520467091…33835509977519710601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.682 Γ— 10⁹⁡(96-digit number)
16822411142104093418…67671019955039421201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.364 Γ— 10⁹⁡(96-digit number)
33644822284208186836…35342039910078842401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.728 Γ— 10⁹⁡(96-digit number)
67289644568416373673…70684079820157684801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.345 Γ— 10⁹⁢(97-digit number)
13457928913683274734…41368159640315369601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.691 Γ— 10⁹⁢(97-digit number)
26915857827366549469…82736319280630739201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.383 Γ— 10⁹⁢(97-digit number)
53831715654733098938…65472638561261478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.076 Γ— 10⁹⁷(98-digit number)
10766343130946619787…30945277122522956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.153 Γ— 10⁹⁷(98-digit number)
21532686261893239575…61890554245045913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.306 Γ— 10⁹⁷(98-digit number)
43065372523786479150…23781108490091827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.613 Γ— 10⁹⁷(98-digit number)
86130745047572958301…47562216980183654401
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:57,991,704 XPMΒ·at block #6,843,416 Β· updates every 60s
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