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Block #2,077,807

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/19/2017, 2:00:41 PM Β· Difficulty 10.8510 Β· 4,766,233 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cfeba33baf22a58b4c112a0279bbe4d9e9fb6bd1411bb41a4419f877ea5f4a02
View on Chainz β†—

Height

#2,077,807

Difficulty

10.851032

Transactions

1

Size

199 B

Version

2

Bits

0ad9dd3f

Nonce

683,614,594

Timestamp

4/19/2017, 2:00:41 PM

Confirmations

4,766,233

Mined by

⛏️ P2SHAMBBiSALDeFTcSQfgCdLjjUrnfnEWq2mHv

Merkle Root

eb12112a6bd13654a1d3850c797e6ba546e08010adebb9aaedfcb4eacdb4c00f
Transactions (1)
Coinbaseeb12112a6bd136…fcb4eacdb4c00f
1 in β†’ 1 out8.4800 XPM109 B
AMBBiSAL…nEWq2mHv
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.

2.096 Γ— 10⁹⁡(96-digit number)
20965449179836836291…51062177398647525441
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
2.096 Γ— 10⁹⁡(96-digit number)
20965449179836836291…51062177398647525441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.193 Γ— 10⁹⁡(96-digit number)
41930898359673672583…02124354797295050881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.386 Γ— 10⁹⁡(96-digit number)
83861796719347345166…04248709594590101761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.677 Γ— 10⁹⁢(97-digit number)
16772359343869469033…08497419189180203521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.354 Γ— 10⁹⁢(97-digit number)
33544718687738938066…16994838378360407041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.708 Γ— 10⁹⁢(97-digit number)
67089437375477876133…33989676756720814081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.341 Γ— 10⁹⁷(98-digit number)
13417887475095575226…67979353513441628161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.683 Γ— 10⁹⁷(98-digit number)
26835774950191150453…35958707026883256321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.367 Γ— 10⁹⁷(98-digit number)
53671549900382300906…71917414053766512641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.073 Γ— 10⁹⁸(99-digit number)
10734309980076460181…43834828107533025281
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:57,996,689 XPMΒ·at block #6,844,039 Β· updates every 60s
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