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Block #85,462

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/27/2013, 11:04:44 AM Β· Difficulty 9.2898 Β· 6,721,886 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1df273bd427857896262ed299c521de7a007998fffc18c9e585d4f519da5da7f
View on Chainz β†—

Height

#85,462

Difficulty

9.289820

Transactions

1

Size

198 B

Version

2

Bits

094a31ad

Nonce

125

Timestamp

7/27/2013, 11:04:44 AM

Confirmations

6,721,886

Mined by

⛏️ P2SHAPDVqt34NEoKmRGPqZSk2zcL1GXWrhV4UM

Merkle Root

b0949168b3bf69eca29cd2565e4dbf2c7861ce3c4a59cad337bf430125cbf766
Transactions (1)
Coinbaseb0949168b3bf69…bf430125cbf766
1 in β†’ 1 out11.5700 XPM110 B
APDVqt34…XWrhV4UM
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.

6.231 Γ— 10⁸⁹(90-digit number)
62314056744922755254…73077133609862390351
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
6.231 Γ— 10⁸⁹(90-digit number)
62314056744922755254…73077133609862390351
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.246 Γ— 10⁹⁰(91-digit number)
12462811348984551050…46154267219724780701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.492 Γ— 10⁹⁰(91-digit number)
24925622697969102101…92308534439449561401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.985 Γ— 10⁹⁰(91-digit number)
49851245395938204203…84617068878899122801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.970 Γ— 10⁹⁰(91-digit number)
99702490791876408407…69234137757798245601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.994 Γ— 10⁹¹(92-digit number)
19940498158375281681…38468275515596491201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.988 Γ— 10⁹¹(92-digit number)
39880996316750563362…76936551031192982401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.976 Γ— 10⁹¹(92-digit number)
79761992633501126725…53873102062385964801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.595 Γ— 10⁹²(93-digit number)
15952398526700225345…07746204124771929601
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:57,702,804 XPMΒ·at block #6,807,347 Β· updates every 60s
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