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Block #2,136,145

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/28/2017, 9:44:21 PM Β· Difficulty 10.8959 Β· 4,700,757 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2810ab0bf4ec830ee7949ab5b03dcd334d463bf38a1a02abb53c89519e9e1d8c
View on Chainz β†—

Height

#2,136,145

Difficulty

10.895897

Transactions

2

Size

722 B

Version

2

Bits

0ae5597c

Nonce

1,427,360,861

Timestamp

5/28/2017, 9:44:21 PM

Confirmations

4,700,757

Mined by

⛏️ P2SHAJVVn2PdUDeFNvfcTUgF8E99NK4z5sZfWw

Merkle Root

8cf25a4a1d1cf33efba57429be6d98afab1951718e7efefdf3c095e3b6474b24
Transactions (2)
Coinbaseb87e724204578b…2a4adc20411de1
1 in β†’ 1 out8.4200 XPM109 B
AJVVn2Pd…4z5sZfWw
6b6a8dc3e7326f…f5368235552a80
3 in β†’ 2 out989.0226 XPM523 B
AM5iAcHi…EaSLASCqAJ28VsS4…Y752EzFP
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.

7.554 Γ— 10⁹⁴(95-digit number)
75549890698244420754…41906469171548025599
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
7.554 Γ— 10⁹⁴(95-digit number)
75549890698244420754…41906469171548025599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.510 Γ— 10⁹⁡(96-digit number)
15109978139648884150…83812938343096051199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.021 Γ— 10⁹⁡(96-digit number)
30219956279297768301…67625876686192102399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.043 Γ— 10⁹⁡(96-digit number)
60439912558595536603…35251753372384204799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.208 Γ— 10⁹⁢(97-digit number)
12087982511719107320…70503506744768409599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.417 Γ— 10⁹⁢(97-digit number)
24175965023438214641…41007013489536819199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.835 Γ— 10⁹⁢(97-digit number)
48351930046876429283…82014026979073638399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.670 Γ— 10⁹⁢(97-digit number)
96703860093752858566…64028053958147276799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.934 Γ— 10⁹⁷(98-digit number)
19340772018750571713…28056107916294553599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.868 Γ— 10⁹⁷(98-digit number)
38681544037501143426…56112215832589107199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,939,508 XPMΒ·at block #6,836,901 Β· updates every 60s
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