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Block #2,153,345

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/9/2017, 2:47:01 PM Β· Difficulty 10.9031 Β· 4,691,821 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3eff720f03e617dc29ad03c5515f553bce512d02b0bfc196cf1eeaf1e6bb9288
View on Chainz β†—

Height

#2,153,345

Difficulty

10.903050

Transactions

2

Size

1.97 KB

Version

2

Bits

0ae72e49

Nonce

238,097,354

Timestamp

6/9/2017, 2:47:01 PM

Confirmations

4,691,821

Mined by

⛏️ P2SHANC1uVEZfTcEYC5F6VbXHVdy5VUhbYK7HN

Merkle Root

57c0d7e41f51da55504009981db1c6a593ccdde1ed31338000a85befac1453ad
Transactions (2)
Coinbasea0b2b26506bff7…a3af56fdf1d526
1 in β†’ 1 out8.4200 XPM110 B
ANC1uVEZ…UhbYK7HN
1f5ae22accf5b2…c4810a0547d8b1
12 in β†’ 1 out339.3526 XPM1.78 KB
AGvdHWSe…5kDa8nuT
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.

4.564 Γ— 10⁹⁡(96-digit number)
45646454538039660426…95402969841648742401
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
4.564 Γ— 10⁹⁡(96-digit number)
45646454538039660426…95402969841648742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.129 Γ— 10⁹⁡(96-digit number)
91292909076079320853…90805939683297484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.825 Γ— 10⁹⁢(97-digit number)
18258581815215864170…81611879366594969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.651 Γ— 10⁹⁢(97-digit number)
36517163630431728341…63223758733189939201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.303 Γ— 10⁹⁢(97-digit number)
73034327260863456683…26447517466379878401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.460 Γ— 10⁹⁷(98-digit number)
14606865452172691336…52895034932759756801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.921 Γ— 10⁹⁷(98-digit number)
29213730904345382673…05790069865519513601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.842 Γ— 10⁹⁷(98-digit number)
58427461808690765346…11580139731039027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.168 Γ— 10⁹⁸(99-digit number)
11685492361738153069…23160279462078054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.337 Γ— 10⁹⁸(99-digit number)
23370984723476306138…46320558924156108801
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:58,005,758 XPMΒ·at block #6,845,165 Β· updates every 60s
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