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Block #557,227

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/22/2014, 7:39:31 PM Β· Difficulty 10.9628 Β· 6,242,257 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
306cc5580b9252f25fa66a66429018af1e0b8a54534468e56db16ac72fdb3e91
View on Chainz β†—

Height

#557,227

Difficulty

10.962797

Transactions

2

Size

2.41 KB

Version

2

Bits

0af679e4

Nonce

30,063,590

Timestamp

5/22/2014, 7:39:31 PM

Confirmations

6,242,257

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1ab4d1f572175b0b5f1d235d4fe6085e0a7018c9e6ca48cb68e56f09be979ed2
Transactions (2)
Coinbaseaa9ae0a2df226a…e4ef9a1722acfa
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
d4c17b3f246990…3c42158a29f350
15 in β†’ 1 out45.0622 XPM2.21 KB
AYfGXBG3…s4uNnsy3
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.

6.733 Γ— 10⁹⁸(99-digit number)
67337260671487676747…23899370880955371521
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
6.733 Γ— 10⁹⁸(99-digit number)
67337260671487676747…23899370880955371521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.346 Γ— 10⁹⁹(100-digit number)
13467452134297535349…47798741761910743041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.693 Γ— 10⁹⁹(100-digit number)
26934904268595070698…95597483523821486081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.386 Γ— 10⁹⁹(100-digit number)
53869808537190141397…91194967047642972161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.077 Γ— 10¹⁰⁰(101-digit number)
10773961707438028279…82389934095285944321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.154 Γ— 10¹⁰⁰(101-digit number)
21547923414876056559…64779868190571888641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.309 Γ— 10¹⁰⁰(101-digit number)
43095846829752113118…29559736381143777281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.619 Γ— 10¹⁰⁰(101-digit number)
86191693659504226236…59119472762287554561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.723 Γ— 10¹⁰¹(102-digit number)
17238338731900845247…18238945524575109121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.447 Γ— 10¹⁰¹(102-digit number)
34476677463801690494…36477891049150218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.895 Γ— 10¹⁰¹(102-digit number)
68953354927603380989…72955782098300436481
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:57,639,914 XPMΒ·at block #6,799,483 Β· updates every 60s
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