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Block #86,863

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2013, 11:03:32 AM Β· Difficulty 9.2846 Β· 6,718,491 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d51cb8f2b6e96ad5c59e2b032407bb6986d09f6b7c5d5bac931f65b3b7bf1a34
View on Chainz β†—

Height

#86,863

Difficulty

9.284580

Transactions

1

Size

204 B

Version

2

Bits

0948da3c

Nonce

22,833

Timestamp

7/28/2013, 11:03:32 AM

Confirmations

6,718,491

Mined by

⛏️ P2SHAXLw2aRPYYPFFpsV5yWkbuXFjuXXd4m397

Merkle Root

095c6152864a569a7de1543e36f63cecb257718994f1354da6a0ce0ae72e7f85
Transactions (1)
Coinbase095c6152864a56…a0ce0ae72e7f85
1 in β†’ 1 out11.5800 XPM109 B
AXLw2aRP…XXd4m397
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.

7.450 Γ— 10¹⁰⁢(107-digit number)
74500527421770395480…66796777676443846501
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
7.450 Γ— 10¹⁰⁢(107-digit number)
74500527421770395480…66796777676443846501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.490 Γ— 10¹⁰⁷(108-digit number)
14900105484354079096…33593555352887693001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.980 Γ— 10¹⁰⁷(108-digit number)
29800210968708158192…67187110705775386001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.960 Γ— 10¹⁰⁷(108-digit number)
59600421937416316384…34374221411550772001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.192 Γ— 10¹⁰⁸(109-digit number)
11920084387483263276…68748442823101544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.384 Γ— 10¹⁰⁸(109-digit number)
23840168774966526553…37496885646203088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.768 Γ— 10¹⁰⁸(109-digit number)
47680337549933053107…74993771292406176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.536 Γ— 10¹⁰⁸(109-digit number)
95360675099866106214…49987542584812352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.907 Γ— 10¹⁰⁹(110-digit number)
19072135019973221242…99975085169624704001
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:57,686,916 XPMΒ·at block #6,805,353 Β· updates every 60s
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