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Block #1,611,869

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2016, 3:47:02 AM Β· Difficulty 10.6055 Β· 5,230,837 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a748546656c6572cff1634a6d48e61a52a9a4f33761a913256feb5ac6dcb0225
View on Chainz β†—

Height

#1,611,869

Difficulty

10.605520

Transactions

1

Size

199 B

Version

2

Bits

0a9b035d

Nonce

1,036,056,494

Timestamp

6/3/2016, 3:47:02 AM

Confirmations

5,230,837

Mined by

⛏️ P2SHAHxsNVXpQxzhhVG2ipZSkqc7ekJYiXzXyH

Merkle Root

700a65f479320fcb957fb9b65801155c201a0888636848a6dfff78ff1feb833c
Transactions (1)
Coinbase700a65f479320f…ff78ff1feb833c
1 in β†’ 1 out8.8800 XPM109 B
AHxsNVXp…JYiXzXyH
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.

4.720 Γ— 10⁹⁴(95-digit number)
47201799467053765276…06590858316213617681
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
4.720 Γ— 10⁹⁴(95-digit number)
47201799467053765276…06590858316213617681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.440 Γ— 10⁹⁴(95-digit number)
94403598934107530553…13181716632427235361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.888 Γ— 10⁹⁡(96-digit number)
18880719786821506110…26363433264854470721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.776 Γ— 10⁹⁡(96-digit number)
37761439573643012221…52726866529708941441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.552 Γ— 10⁹⁡(96-digit number)
75522879147286024442…05453733059417882881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.510 Γ— 10⁹⁢(97-digit number)
15104575829457204888…10907466118835765761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.020 Γ— 10⁹⁢(97-digit number)
30209151658914409777…21814932237671531521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.041 Γ— 10⁹⁢(97-digit number)
60418303317828819554…43629864475343063041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.208 Γ— 10⁹⁷(98-digit number)
12083660663565763910…87259728950686126081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.416 Γ— 10⁹⁷(98-digit number)
24167321327131527821…74519457901372252161
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:57,985,998 XPMΒ·at block #6,842,705 Β· updates every 60s
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