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Block #560,985

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2014, 5:31:22 AM Β· Difficulty 10.9650 Β· 6,251,778 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a3e50c8a58b0760b1903725be53bf3f8ee2c4b2a0ab4676dfb917ca71ec5713c
View on Chainz β†—

Height

#560,985

Difficulty

10.964964

Transactions

1

Size

207 B

Version

2

Bits

0af707dc

Nonce

262,305,654

Timestamp

5/25/2014, 5:31:22 AM

Confirmations

6,251,778

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b6dff6b5e73173c8104a862b2f7e96db3a13861e6e491f2973ebe79b6e18af71
Transactions (1)
Coinbaseb6dff6b5e73173…ebe79b6e18af71
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

6.006 Γ— 10⁹⁢(97-digit number)
60061582238542105031…26514540086133130801
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
6.006 Γ— 10⁹⁢(97-digit number)
60061582238542105031…26514540086133130801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.201 Γ— 10⁹⁷(98-digit number)
12012316447708421006…53029080172266261601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.402 Γ— 10⁹⁷(98-digit number)
24024632895416842012…06058160344532523201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.804 Γ— 10⁹⁷(98-digit number)
48049265790833684024…12116320689065046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.609 Γ— 10⁹⁷(98-digit number)
96098531581667368049…24232641378130092801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.921 Γ— 10⁹⁸(99-digit number)
19219706316333473609…48465282756260185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.843 Γ— 10⁹⁸(99-digit number)
38439412632666947219…96930565512520371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.687 Γ— 10⁹⁸(99-digit number)
76878825265333894439…93861131025040742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.537 Γ— 10⁹⁹(100-digit number)
15375765053066778887…87722262050081484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.075 Γ— 10⁹⁹(100-digit number)
30751530106133557775…75444524100162969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.150 Γ— 10⁹⁹(100-digit number)
61503060212267115551…50889048200325939201
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:57,746,141 XPMΒ·at block #6,812,762 Β· updates every 60s
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