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Block #219,989

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/20/2013, 7:02:51 PM Β· Difficulty 9.9349 Β· 6,590,429 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
efa9082d95d46b95cadcddfca282035268cf0f77df5761a4a8afab6ef3b18d0d
View on Chainz β†—

Height

#219,989

Difficulty

9.934915

Transactions

1

Size

204 B

Version

2

Bits

09ef5697

Nonce

16,778,242

Timestamp

10/20/2013, 7:02:51 PM

Confirmations

6,590,429

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

8640a0f2afb491b868d77e46993ffdacb373a4faf630af51dbcdebadd9771373
Transactions (1)
Coinbase8640a0f2afb491…cdebadd9771373
1 in β†’ 1 out10.1200 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.431 Γ— 10⁹⁰(91-digit number)
24313986512444096941…12598631319952556871
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
2.431 Γ— 10⁹⁰(91-digit number)
24313986512444096941…12598631319952556871
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.862 Γ— 10⁹⁰(91-digit number)
48627973024888193882…25197262639905113741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.725 Γ— 10⁹⁰(91-digit number)
97255946049776387765…50394525279810227481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.945 Γ— 10⁹¹(92-digit number)
19451189209955277553…00789050559620454961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.890 Γ— 10⁹¹(92-digit number)
38902378419910555106…01578101119240909921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.780 Γ— 10⁹¹(92-digit number)
77804756839821110212…03156202238481819841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.556 Γ— 10⁹²(93-digit number)
15560951367964222042…06312404476963639681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.112 Γ— 10⁹²(93-digit number)
31121902735928444085…12624808953927279361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.224 Γ— 10⁹²(93-digit number)
62243805471856888170…25249617907854558721
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:57,727,425 XPMΒ·at block #6,810,417 Β· updates every 60s
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