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Block #1,075,115

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2015, 11:02:27 AM Β· Difficulty 10.7477 Β· 5,731,787 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ed2f599703e2974c1900bed2710bb19aa997b6352d0571ea6370ad5a9cda1105
View on Chainz β†—

Height

#1,075,115

Difficulty

10.747721

Transactions

1

Size

199 B

Version

2

Bits

0abf6aab

Nonce

949,311,141

Timestamp

5/25/2015, 11:02:27 AM

Confirmations

5,731,787

Mined by

⛏️ P2SHAJitpuBFBWRraKw6JNZ4K3FnMosUNZF3e4

Merkle Root

64f090dc9c274333e80b4b83c56d9ceed0dcb83315948e8905d053278242c896
Transactions (1)
Coinbase64f090dc9c2743…d053278242c896
1 in β†’ 1 out8.6400 XPM109 B
AJitpuBF…sUNZF3e4
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.

1.231 Γ— 10⁹⁡(96-digit number)
12318610413351726719…80637488604528773201
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
1.231 Γ— 10⁹⁡(96-digit number)
12318610413351726719…80637488604528773201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.463 Γ— 10⁹⁡(96-digit number)
24637220826703453438…61274977209057546401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.927 Γ— 10⁹⁡(96-digit number)
49274441653406906876…22549954418115092801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.854 Γ— 10⁹⁡(96-digit number)
98548883306813813752…45099908836230185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.970 Γ— 10⁹⁢(97-digit number)
19709776661362762750…90199817672460371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.941 Γ— 10⁹⁢(97-digit number)
39419553322725525501…80399635344920742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.883 Γ— 10⁹⁢(97-digit number)
78839106645451051002…60799270689841484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.576 Γ— 10⁹⁷(98-digit number)
15767821329090210200…21598541379682969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.153 Γ— 10⁹⁷(98-digit number)
31535642658180420400…43197082759365939201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.307 Γ— 10⁹⁷(98-digit number)
63071285316360840801…86394165518731878401
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:57,699,326 XPMΒ·at block #6,806,901 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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