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Block #2,131,756

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 7:54:19 AM Β· Difficulty 10.9102 Β· 4,711,400 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a29b255dabc7a71ae270c9eec2969aafb7e170dcac8a228b388b300f6cdd6df2
View on Chainz β†—

Height

#2,131,756

Difficulty

10.910242

Transactions

1

Size

199 B

Version

2

Bits

0ae905a4

Nonce

251,157,162

Timestamp

5/25/2017, 7:54:19 AM

Confirmations

4,711,400

Mined by

⛏️ P2SHAdFD71UcpWesqP7Ne6xvxaDAMw3vhwEtnw

Merkle Root

51dc4ddd4c2971eeff04ef6f678e1abb57a7f36392696e87ce05dfa33ebbe4c1
Transactions (1)
Coinbase51dc4ddd4c2971…05dfa33ebbe4c1
1 in β†’ 1 out8.3900 XPM109 B
AdFD71Uc…3vhwEtnw
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.

5.763 Γ— 10⁹⁡(96-digit number)
57632330032703770688…31166436835750250881
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
5.763 Γ— 10⁹⁡(96-digit number)
57632330032703770688…31166436835750250881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.152 Γ— 10⁹⁢(97-digit number)
11526466006540754137…62332873671500501761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.305 Γ— 10⁹⁢(97-digit number)
23052932013081508275…24665747343001003521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.610 Γ— 10⁹⁢(97-digit number)
46105864026163016550…49331494686002007041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.221 Γ— 10⁹⁢(97-digit number)
92211728052326033101…98662989372004014081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.844 Γ— 10⁹⁷(98-digit number)
18442345610465206620…97325978744008028161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.688 Γ— 10⁹⁷(98-digit number)
36884691220930413240…94651957488016056321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.376 Γ— 10⁹⁷(98-digit number)
73769382441860826480…89303914976032112641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.475 Γ— 10⁹⁸(99-digit number)
14753876488372165296…78607829952064225281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.950 Γ— 10⁹⁸(99-digit number)
29507752976744330592…57215659904128450561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.901 Γ— 10⁹⁸(99-digit number)
59015505953488661184…14431319808256901121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,989,614 XPMΒ·at block #6,843,155 Β· updates every 60s
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