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Block #1,161,689

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2015, 8:29:21 PM Β· Difficulty 10.9365 Β· 5,644,780 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dde4037fbfcb2d9c67f53e026604082f5cfeccff8c010ac43845385cac36ce7f
View on Chainz β†—

Height

#1,161,689

Difficulty

10.936535

Transactions

2

Size

2.59 KB

Version

2

Bits

0aefc0be

Nonce

1,077,149,485

Timestamp

7/19/2015, 8:29:21 PM

Confirmations

5,644,780

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

66d373340ec457e86ef1eb09878d386698a94b84559e1026a1dc2af9bff70473
Transactions (2)
Coinbased0fde4aabc81c8…c45b74df109377
1 in β†’ 1 out8.3900 XPM116 B
AJCEY9yy…tg97E6zm
cbe93e05c76338…e8e97c956fe11f
16 in β†’ 2 out299.9593 XPM2.39 KB
AaxKBWi9…Se8hw7s8AMP7EGhn…hgQDQGEc
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.

3.390 Γ— 10⁹⁡(96-digit number)
33901081876412210339…14255676410802505281
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
3.390 Γ— 10⁹⁡(96-digit number)
33901081876412210339…14255676410802505281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.780 Γ— 10⁹⁡(96-digit number)
67802163752824420678…28511352821605010561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.356 Γ— 10⁹⁢(97-digit number)
13560432750564884135…57022705643210021121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.712 Γ— 10⁹⁢(97-digit number)
27120865501129768271…14045411286420042241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.424 Γ— 10⁹⁢(97-digit number)
54241731002259536543…28090822572840084481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.084 Γ— 10⁹⁷(98-digit number)
10848346200451907308…56181645145680168961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.169 Γ— 10⁹⁷(98-digit number)
21696692400903814617…12363290291360337921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.339 Γ— 10⁹⁷(98-digit number)
43393384801807629234…24726580582720675841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.678 Γ— 10⁹⁷(98-digit number)
86786769603615258468…49453161165441351681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.735 Γ— 10⁹⁸(99-digit number)
17357353920723051693…98906322330882703361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.471 Γ— 10⁹⁸(99-digit number)
34714707841446103387…97812644661765406721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
6.942 Γ— 10⁹⁸(99-digit number)
69429415682892206775…95625289323530813441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,695,845 XPMΒ·at block #6,806,468 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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