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Block #72,508

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 12:35:09 AM Β· Difficulty 8.9941 Β· 6,737,403 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f2dae8d46c53c40033a6029312d95364f24d36df3ffc5d7eadf737739a95c43
View on Chainz β†—

Height

#72,508

Difficulty

8.994121

Transactions

1

Size

196 B

Version

2

Bits

08fe7ebf

Nonce

601

Timestamp

7/21/2013, 12:35:09 AM

Confirmations

6,737,403

Mined by

⛏️ P2SHALD4vzJs4Zwqrn14ZxtLe9UeDdGRCXP6ri

Merkle Root

4fa217b2ef3cdf470c77dc30aa86f2efcc87a7c6072d985d36cd5830bf9b48ba
Transactions (1)
Coinbase4fa217b2ef3cdf…cd5830bf9b48ba
1 in β†’ 1 out12.3400 XPM110 B
ALD4vzJs…GRCXP6ri
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.

5.604 Γ— 10⁸⁡(86-digit number)
56046142911913600741…14476690027293571651
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
5.604 Γ— 10⁸⁡(86-digit number)
56046142911913600741…14476690027293571651
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.120 Γ— 10⁸⁢(87-digit number)
11209228582382720148…28953380054587143301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.241 Γ— 10⁸⁢(87-digit number)
22418457164765440296…57906760109174286601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.483 Γ— 10⁸⁢(87-digit number)
44836914329530880593…15813520218348573201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.967 Γ— 10⁸⁢(87-digit number)
89673828659061761186…31627040436697146401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.793 Γ— 10⁸⁷(88-digit number)
17934765731812352237…63254080873394292801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.586 Γ— 10⁸⁷(88-digit number)
35869531463624704474…26508161746788585601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.173 Γ— 10⁸⁷(88-digit number)
71739062927249408948…53016323493577171201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,723,372 XPMΒ·at block #6,809,910 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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