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Block #59,907

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 4:58:12 AM Β· Difficulty 8.9670 Β· 6,750,141 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7113067769b2f8d573a70eec2d733b672607c76bf9e27692f2895528402b4cf7
View on Chainz β†—

Height

#59,907

Difficulty

8.966975

Transactions

1

Size

199 B

Version

2

Bits

08f78bb3

Nonce

0

Timestamp

7/18/2013, 4:58:12 AM

Confirmations

6,750,141

Mined by

⛏️ P2SHAMqqcfJzqhuzkSnqmTVWQTibJDKd59315M

Merkle Root

ba9da94219d4fa01bf8d2adeaa800a89c6831ae473a7e051e7330fac72486a1e
Transactions (1)
Coinbaseba9da94219d4fa…330fac72486a1e
1 in β†’ 1 out12.4200 XPM110 B
AMqqcfJz…Kd59315M
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.

5.450 Γ— 10⁹¹(92-digit number)
54503356500863327526…95268248081156909909
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.450 Γ— 10⁹¹(92-digit number)
54503356500863327526…95268248081156909909
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.090 Γ— 10⁹²(93-digit number)
10900671300172665505…90536496162313819819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.180 Γ— 10⁹²(93-digit number)
21801342600345331010…81072992324627639639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.360 Γ— 10⁹²(93-digit number)
43602685200690662021…62145984649255279279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.720 Γ— 10⁹²(93-digit number)
87205370401381324043…24291969298510558559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.744 Γ— 10⁹³(94-digit number)
17441074080276264808…48583938597021117119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.488 Γ— 10⁹³(94-digit number)
34882148160552529617…97167877194042234239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.976 Γ— 10⁹³(94-digit number)
69764296321105059234…94335754388084468479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.395 Γ— 10⁹⁴(95-digit number)
13952859264221011846…88671508776168936959
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,724,456 XPMΒ·at block #6,810,047 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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