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Block #1,451,406

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/11/2016, 3:48:28 AM Β· Difficulty 10.7427 Β· 5,373,605 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f5f30619eecec2d6f4e7cec6dc6aad3757de4815a60d8afedfc331caac2015a3
View on Chainz β†—

Height

#1,451,406

Difficulty

10.742655

Transactions

1

Size

243 B

Version

2

Bits

0abe1ea0

Nonce

2,528,026,920

Timestamp

2/11/2016, 3:48:28 AM

Confirmations

5,373,605

Mined by

⛏️ P2SHAbNVgXWJCnXJ31RnMLH7T3xjBzg3uNfMnj

Merkle Root

1f39edbf5f4d46a25b2e3163572ee1feba94f1b45c20c9a655795f26779bdd3a
Transactions (1)
Coinbase1f39edbf5f4d46…795f26779bdd3a
1 in β†’ 2 out8.6500 XPM152 B
AbNVgXWJ…g3uNfMnjALPu3s2c…EJXLjVFh
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.

1.671 Γ— 10⁹⁷(98-digit number)
16713333209621367836…60352618217901045761
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
1.671 Γ— 10⁹⁷(98-digit number)
16713333209621367836…60352618217901045761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.342 Γ— 10⁹⁷(98-digit number)
33426666419242735673…20705236435802091521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.685 Γ— 10⁹⁷(98-digit number)
66853332838485471347…41410472871604183041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.337 Γ— 10⁹⁸(99-digit number)
13370666567697094269…82820945743208366081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.674 Γ— 10⁹⁸(99-digit number)
26741333135394188538…65641891486416732161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.348 Γ— 10⁹⁸(99-digit number)
53482666270788377077…31283782972833464321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.069 Γ— 10⁹⁹(100-digit number)
10696533254157675415…62567565945666928641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.139 Γ— 10⁹⁹(100-digit number)
21393066508315350831…25135131891333857281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.278 Γ— 10⁹⁹(100-digit number)
42786133016630701662…50270263782667714561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.557 Γ— 10⁹⁹(100-digit number)
85572266033261403324…00540527565335429121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,844,173 XPMΒ·at block #6,825,010 Β· updates every 60s
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