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Block #1,106,808

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/15/2015, 12:47:22 PM Β· Difficulty 10.8078 Β· 5,702,564 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2e6dc2f26dfa9702e067d14abc8ca7e05b50d480222e6f5ce3795bc39f7a37a
View on Chainz β†—

Height

#1,106,808

Difficulty

10.807798

Transactions

2

Size

53.62 KB

Version

2

Bits

0acecbdd

Nonce

554,062,875

Timestamp

6/15/2015, 12:47:22 PM

Confirmations

5,702,564

Mined by

⛏️ P2SHAMX8uKKNNz4n8am36eNJX9bMHSLNt9aLdH

Merkle Root

dc5d7f6d1298c38c70e47c239795a805f2881b643e26db0ac760ac5b43723b08
Transactions (2)
Coinbase56569cd15815e3…06140f081e337a
1 in β†’ 1 out9.1300 XPM110 B
AMX8uKKN…LNt9aLdH
00395b262302be…c4eb0b5adba6c2
369 in β†’ 2 out500.0000 XPM53.42 KB
AWNJsA8B…1aMvpFXMAPjrvGg2…41Ezfo5w
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.

4.532 Γ— 10⁹⁡(96-digit number)
45325689213372832859…43367075656937830401
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
4.532 Γ— 10⁹⁡(96-digit number)
45325689213372832859…43367075656937830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.065 Γ— 10⁹⁡(96-digit number)
90651378426745665718…86734151313875660801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.813 Γ— 10⁹⁢(97-digit number)
18130275685349133143…73468302627751321601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.626 Γ— 10⁹⁢(97-digit number)
36260551370698266287…46936605255502643201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.252 Γ— 10⁹⁢(97-digit number)
72521102741396532575…93873210511005286401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.450 Γ— 10⁹⁷(98-digit number)
14504220548279306515…87746421022010572801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.900 Γ— 10⁹⁷(98-digit number)
29008441096558613030…75492842044021145601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.801 Γ— 10⁹⁷(98-digit number)
58016882193117226060…50985684088042291201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.160 Γ— 10⁹⁸(99-digit number)
11603376438623445212…01971368176084582401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.320 Γ— 10⁹⁸(99-digit number)
23206752877246890424…03942736352169164801
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:57,719,045 XPMΒ·at block #6,809,371 Β· updates every 60s
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