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Block #1,110,630

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/16/2015, 4:50:18 PM Β· Difficulty 10.8744 Β· 5,701,539 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
757c5b9daf74fe396326563c842a40f82d6872754a4ee1efe76f39c792d8e12b
View on Chainz β†—

Height

#1,110,630

Difficulty

10.874354

Transactions

2

Size

2.15 KB

Version

2

Bits

0adfd5a3

Nonce

42,317,041

Timestamp

6/16/2015, 4:50:18 PM

Confirmations

5,701,539

Mined by

⛏️ P2SHAMGUshFxA1EqRQdgcd5Uuhy4yC3WnYJoPA

Merkle Root

a2e2b7e431856a0e13f7778a6d87ab938f4a24d399bbb514fd5f5549289743a4
Transactions (2)
Coinbase805178a1723041…abfd5b096c8983
1 in β†’ 1 out8.5500 XPM110 B
AMGUshFx…3WnYJoPA
a4667812108f99…111a72e87868ff
13 in β†’ 2 out2235.4228 XPM1.95 KB
APpxUz8m…YzdT5d4QASmDyq6d…zHF7z7LT
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.

6.632 Γ— 10⁹³(94-digit number)
66323885735384700140…53460429877787197441
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
6.632 Γ— 10⁹³(94-digit number)
66323885735384700140…53460429877787197441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.326 Γ— 10⁹⁴(95-digit number)
13264777147076940028…06920859755574394881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.652 Γ— 10⁹⁴(95-digit number)
26529554294153880056…13841719511148789761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.305 Γ— 10⁹⁴(95-digit number)
53059108588307760112…27683439022297579521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.061 Γ— 10⁹⁡(96-digit number)
10611821717661552022…55366878044595159041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.122 Γ— 10⁹⁡(96-digit number)
21223643435323104045…10733756089190318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.244 Γ— 10⁹⁡(96-digit number)
42447286870646208090…21467512178380636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.489 Γ— 10⁹⁡(96-digit number)
84894573741292416180…42935024356761272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.697 Γ— 10⁹⁢(97-digit number)
16978914748258483236…85870048713522544641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.395 Γ— 10⁹⁢(97-digit number)
33957829496516966472…71740097427045089281
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:57,741,371 XPMΒ·at block #6,812,168 Β· updates every 60s
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