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Block #88,718

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/29/2013, 8:09:15 PM Β· Difficulty 9.2659 Β· 6,708,094 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0cd165d61191317071ee552d8dbc4e6600f6f1d4ad9640af9242fb8a9140cf35
View on Chainz β†—

Height

#88,718

Difficulty

9.265883

Transactions

1

Size

203 B

Version

2

Bits

094410e3

Nonce

12,144

Timestamp

7/29/2013, 8:09:15 PM

Confirmations

6,708,094

Mined by

⛏️ P2SHATzEHZ7ayQf8Js5VJS7Me8qrBi2eAGweip

Merkle Root

fd2116b8ed62794682b615bab21d9c612b2d631828cbbbbfdb0b1f227b9ba504
Transactions (1)
Coinbasefd2116b8ed6279…0b1f227b9ba504
1 in β†’ 1 out11.6300 XPM109 B
ATzEHZ7a…2eAGweip
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.

6.547 Γ— 10¹⁰⁴(105-digit number)
65476597783779505646…38907440046345948251
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
6.547 Γ— 10¹⁰⁴(105-digit number)
65476597783779505646…38907440046345948251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.309 Γ— 10¹⁰⁡(106-digit number)
13095319556755901129…77814880092691896501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.619 Γ— 10¹⁰⁡(106-digit number)
26190639113511802258…55629760185383793001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.238 Γ— 10¹⁰⁡(106-digit number)
52381278227023604517…11259520370767586001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.047 Γ— 10¹⁰⁢(107-digit number)
10476255645404720903…22519040741535172001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.095 Γ— 10¹⁰⁢(107-digit number)
20952511290809441806…45038081483070344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.190 Γ— 10¹⁰⁢(107-digit number)
41905022581618883613…90076162966140688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.381 Γ— 10¹⁰⁢(107-digit number)
83810045163237767227…80152325932281376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.676 Γ— 10¹⁰⁷(108-digit number)
16762009032647553445…60304651864562752001
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:57,618,511 XPMΒ·at block #6,796,811 Β· updates every 60s
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