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Block #241,572

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/3/2013, 6:58:31 AM Β· Difficulty 9.9582 Β· 6,568,003 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
52955e6ff25bb147024e8a38cf20b34a6a289d2727fff512eab7628ae5c752ad
View on Chainz β†—

Height

#241,572

Difficulty

9.958172

Transactions

1

Size

199 B

Version

2

Bits

09f54ac3

Nonce

86,998

Timestamp

11/3/2013, 6:58:31 AM

Confirmations

6,568,003

Mined by

⛏️ P2SHAbz38twNnWn3z2rrYPRTzbKGWSVkCgPh1J

Merkle Root

16335843ded5db5b1e9cd60cde14fa6f8ff8736268f14f9a7b94ddbe772f42a3
Transactions (1)
Coinbase16335843ded5db…94ddbe772f42a3
1 in β†’ 1 out10.0700 XPM109 B
Abz38twN…VkCgPh1J
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.

2.819 Γ— 10⁹³(94-digit number)
28192142512017174515…26687869727184522239
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
2.819 Γ— 10⁹³(94-digit number)
28192142512017174515…26687869727184522239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.638 Γ— 10⁹³(94-digit number)
56384285024034349030…53375739454369044479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.127 Γ— 10⁹⁴(95-digit number)
11276857004806869806…06751478908738088959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.255 Γ— 10⁹⁴(95-digit number)
22553714009613739612…13502957817476177919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.510 Γ— 10⁹⁴(95-digit number)
45107428019227479224…27005915634952355839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.021 Γ— 10⁹⁴(95-digit number)
90214856038454958448…54011831269904711679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.804 Γ— 10⁹⁡(96-digit number)
18042971207690991689…08023662539809423359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.608 Γ— 10⁹⁡(96-digit number)
36085942415381983379…16047325079618846719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.217 Γ— 10⁹⁡(96-digit number)
72171884830763966758…32094650159237693439
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:57,720,677 XPMΒ·at block #6,809,574 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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