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Block #919,161

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/1/2015, 10:55:50 PM Β· Difficulty 10.9213 Β· 5,877,679 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b11dab50532123cc7a37cf2a2b6ae7c84a67732e7cb4147c3798c72222f5b4e8
View on Chainz β†—

Height

#919,161

Difficulty

10.921265

Transactions

2

Size

3.74 KB

Version

2

Bits

0aebd805

Nonce

141,706,353

Timestamp

2/1/2015, 10:55:50 PM

Confirmations

5,877,679

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

04d7e89201234396b99ea27a2eae929eaa28be3f74fad021dd0056ed7d39312a
Transactions (2)
Coinbase01d4e464f58218…4835f7183146c8
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
d7e73b7083b8e0…e138828413e41f
24 in β†’ 2 out1174.3719 XPM3.54 KB
AW2KFbif…yQ9peR51ASF4nHLe…RxjNCpDa
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.

5.652 Γ— 10⁹⁷(98-digit number)
56526852846697731394…66717624750699768321
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
5.652 Γ— 10⁹⁷(98-digit number)
56526852846697731394…66717624750699768321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.130 Γ— 10⁹⁸(99-digit number)
11305370569339546278…33435249501399536641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.261 Γ— 10⁹⁸(99-digit number)
22610741138679092557…66870499002799073281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.522 Γ— 10⁹⁸(99-digit number)
45221482277358185115…33740998005598146561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.044 Γ— 10⁹⁸(99-digit number)
90442964554716370231…67481996011196293121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.808 Γ— 10⁹⁹(100-digit number)
18088592910943274046…34963992022392586241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.617 Γ— 10⁹⁹(100-digit number)
36177185821886548092…69927984044785172481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.235 Γ— 10⁹⁹(100-digit number)
72354371643773096185…39855968089570344961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.447 Γ— 10¹⁰⁰(101-digit number)
14470874328754619237…79711936179140689921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.894 Γ— 10¹⁰⁰(101-digit number)
28941748657509238474…59423872358281379841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.788 Γ— 10¹⁰⁰(101-digit number)
57883497315018476948…18847744716562759681
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:57,618,732 XPMΒ·at block #6,796,839 Β· updates every 60s
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