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Block #1,612,851

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2016, 9:13:24 PM Β· Difficulty 10.6005 Β· 5,229,406 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a41064eddad4a4a1cedf40b8a3cc201646b4f585ad5724f61034b0f942953ff9
View on Chainz β†—

Height

#1,612,851

Difficulty

10.600531

Transactions

1

Size

199 B

Version

2

Bits

0a99bc6d

Nonce

629,094,764

Timestamp

6/3/2016, 9:13:24 PM

Confirmations

5,229,406

Mined by

⛏️ P2SHAdoAS3YHMH2BGCbb9hmVDtMT7ezhQuzoR6

Merkle Root

322ed60e65016e11e67e267aea838e199552570b92b2ca9a0ff5dc2bbd7caa30
Transactions (1)
Coinbase322ed60e65016e…f5dc2bbd7caa30
1 in β†’ 1 out8.8900 XPM109 B
AdoAS3YH…zhQuzoR6
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.

3.872 Γ— 10⁹⁡(96-digit number)
38726259099432669932…90086484691216103681
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
3.872 Γ— 10⁹⁡(96-digit number)
38726259099432669932…90086484691216103681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.745 Γ— 10⁹⁡(96-digit number)
77452518198865339865…80172969382432207361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.549 Γ— 10⁹⁢(97-digit number)
15490503639773067973…60345938764864414721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.098 Γ— 10⁹⁢(97-digit number)
30981007279546135946…20691877529728829441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.196 Γ— 10⁹⁢(97-digit number)
61962014559092271892…41383755059457658881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.239 Γ— 10⁹⁷(98-digit number)
12392402911818454378…82767510118915317761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.478 Γ— 10⁹⁷(98-digit number)
24784805823636908756…65535020237830635521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.956 Γ— 10⁹⁷(98-digit number)
49569611647273817513…31070040475661271041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.913 Γ— 10⁹⁷(98-digit number)
99139223294547635027…62140080951322542081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.982 Γ— 10⁹⁸(99-digit number)
19827844658909527005…24280161902645084161
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:57,982,453 XPMΒ·at block #6,842,256 Β· updates every 60s
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