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Block #1,109,128

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/16/2015, 5:34:58 AM Β· Difficulty 10.8519 Β· 5,718,230 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fde68dd072f41843f12ba9f50184a8ebe2aa2dedde84f9614e562ee3c6cb6317
View on Chainz β†—

Height

#1,109,128

Difficulty

10.851902

Transactions

2

Size

1017 B

Version

2

Bits

0ada163c

Nonce

686,471,709

Timestamp

6/16/2015, 5:34:58 AM

Confirmations

5,718,230

Mined by

⛏️ P2SHAeFXijxwLhyxyvvas979iGFZUeWyX4ANVF

Merkle Root

23de8ba8c9c9dd93f80742d66f8e85245a124cce2d3d3c02b3e7a7db0636c445
Transactions (2)
Coinbasef96eed9714bb59…04d444eb906004
1 in β†’ 1 out8.9700 XPM110 B
AeFXijxw…WyX4ANVF
2be07901ff7652…919065a2ced446
5 in β†’ 2 out540.0000 XPM817 B
ATHsJgj2…b3PvjTWkAdc72rEv…hmWLEs7R
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.

5.094 Γ— 10⁹³(94-digit number)
50947640225086775339…01857930879793331301
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
5.094 Γ— 10⁹³(94-digit number)
50947640225086775339…01857930879793331301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.018 Γ— 10⁹⁴(95-digit number)
10189528045017355067…03715861759586662601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.037 Γ— 10⁹⁴(95-digit number)
20379056090034710135…07431723519173325201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.075 Γ— 10⁹⁴(95-digit number)
40758112180069420271…14863447038346650401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.151 Γ— 10⁹⁴(95-digit number)
81516224360138840543…29726894076693300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.630 Γ— 10⁹⁡(96-digit number)
16303244872027768108…59453788153386601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.260 Γ— 10⁹⁡(96-digit number)
32606489744055536217…18907576306773203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.521 Γ— 10⁹⁡(96-digit number)
65212979488111072434…37815152613546406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.304 Γ— 10⁹⁢(97-digit number)
13042595897622214486…75630305227092812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.608 Γ— 10⁹⁢(97-digit number)
26085191795244428973…51260610454185625601
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:57,862,963 XPMΒ·at block #6,827,357 Β· updates every 60s
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