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Block #86,875

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2013, 11:16:38 AM Β· Difficulty 9.2846 Β· 6,722,231 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8294656f87c633541e03960a0f4fe279a18249e821f80030f906fea389cf08fa
View on Chainz β†—

Height

#86,875

Difficulty

9.284609

Transactions

1

Size

198 B

Version

2

Bits

0948dc1f

Nonce

230,133

Timestamp

7/28/2013, 11:16:38 AM

Confirmations

6,722,231

Mined by

⛏️ P2SHAWuDuxGXKEXYj7RYhx64EdJKzBtLDpHWp7

Merkle Root

603f488d12a601374648ce6214cf231025b03d7220acb3c4cf7542ae13421cf1
Transactions (1)
Coinbase603f488d12a601…7542ae13421cf1
1 in β†’ 1 out11.5800 XPM109 B
AWuDuxGX…tLDpHWp7
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.

1.234 Γ— 10⁹³(94-digit number)
12344411956424747310…27147661799128541061
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
1.234 Γ— 10⁹³(94-digit number)
12344411956424747310…27147661799128541061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.468 Γ— 10⁹³(94-digit number)
24688823912849494621…54295323598257082121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.937 Γ— 10⁹³(94-digit number)
49377647825698989243…08590647196514164241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.875 Γ— 10⁹³(94-digit number)
98755295651397978487…17181294393028328481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.975 Γ— 10⁹⁴(95-digit number)
19751059130279595697…34362588786056656961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.950 Γ— 10⁹⁴(95-digit number)
39502118260559191394…68725177572113313921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.900 Γ— 10⁹⁴(95-digit number)
79004236521118382789…37450355144226627841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.580 Γ— 10⁹⁡(96-digit number)
15800847304223676557…74900710288453255681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.160 Γ— 10⁹⁡(96-digit number)
31601694608447353115…49801420576906511361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,716,903 XPMΒ·at block #6,809,105 Β· updates every 60s
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