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Block #72,207

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 10:48:46 PM Β· Difficulty 8.9939 Β· 6,744,394 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b4b1cccdc29060ce84dffbbb5a0e66e11bef9d5968295491488a9d5bf6a06bd0
View on Chainz β†—

Height

#72,207

Difficulty

8.993881

Transactions

1

Size

203 B

Version

2

Bits

08fe6eff

Nonce

35

Timestamp

7/20/2013, 10:48:46 PM

Confirmations

6,744,394

Mined by

⛏️ P2SHAH7Eh9GYMSnm23owcXVdfkeuiPK86X1CDg

Merkle Root

fb19224d39c1c63363b96c8518d8266d8658a7533d55832206b9d901f3f218f2
Transactions (1)
Coinbasefb19224d39c1c6…b9d901f3f218f2
1 in β†’ 1 out12.3500 XPM110 B
AH7Eh9GY…K86X1CDg
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.

2.031 Γ— 10¹⁰²(103-digit number)
20310431223793470007…37109030419893888421
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
2.031 Γ— 10¹⁰²(103-digit number)
20310431223793470007…37109030419893888421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.062 Γ— 10¹⁰²(103-digit number)
40620862447586940015…74218060839787776841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.124 Γ— 10¹⁰²(103-digit number)
81241724895173880030…48436121679575553681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.624 Γ— 10¹⁰³(104-digit number)
16248344979034776006…96872243359151107361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.249 Γ— 10¹⁰³(104-digit number)
32496689958069552012…93744486718302214721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.499 Γ— 10¹⁰³(104-digit number)
64993379916139104024…87488973436604429441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.299 Γ— 10¹⁰⁴(105-digit number)
12998675983227820804…74977946873208858881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.599 Γ— 10¹⁰⁴(105-digit number)
25997351966455641609…49955893746417717761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.199 Γ— 10¹⁰⁴(105-digit number)
51994703932911283219…99911787492835435521
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:57,776,934 XPMΒ·at block #6,816,600 Β· updates every 60s
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