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Block #86,683

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2013, 7:47:29 AM Β· Difficulty 9.2868 Β· 6,712,761 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3fc7a4e8045f46d615a6fbeb0701af679933d68e108248f5021c0d74da3cb144
View on Chainz β†—

Height

#86,683

Difficulty

9.286837

Transactions

1

Size

204 B

Version

2

Bits

09496e25

Nonce

17,988

Timestamp

7/28/2013, 7:47:29 AM

Confirmations

6,712,761

Mined by

⛏️ P2SHAXLw2aRPYYPFFpsV5yWkbuXFjuXXd4m397

Merkle Root

c1608188db2da2654547242947c1330148a6d2fe14637d71579ae3e60365eaa6
Transactions (1)
Coinbasec1608188db2da2…9ae3e60365eaa6
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.

1.268 Γ— 10¹⁰⁷(108-digit number)
12680598586872833889…08572848425464286471
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
1.268 Γ— 10¹⁰⁷(108-digit number)
12680598586872833889…08572848425464286471
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.536 Γ— 10¹⁰⁷(108-digit number)
25361197173745667778…17145696850928572941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.072 Γ— 10¹⁰⁷(108-digit number)
50722394347491335557…34291393701857145881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.014 Γ— 10¹⁰⁸(109-digit number)
10144478869498267111…68582787403714291761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.028 Γ— 10¹⁰⁸(109-digit number)
20288957738996534223…37165574807428583521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.057 Γ— 10¹⁰⁸(109-digit number)
40577915477993068446…74331149614857167041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.115 Γ— 10¹⁰⁸(109-digit number)
81155830955986136892…48662299229714334081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.623 Γ— 10¹⁰⁹(110-digit number)
16231166191197227378…97324598459428668161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.246 Γ— 10¹⁰⁹(110-digit number)
32462332382394454756…94649196918857336321
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:57,639,604 XPMΒ·at block #6,799,443 Β· updates every 60s
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