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Block #567,759

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/29/2014, 10:36:04 PM Β· Difficulty 10.9651 Β· 6,242,528 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
08a5ff44ab698fbacd06b5728cb740057ad2c3f79a84dc6217c50cecc7740623
View on Chainz β†—

Height

#567,759

Difficulty

10.965105

Transactions

2

Size

433 B

Version

2

Bits

0af71120

Nonce

311,441,875

Timestamp

5/29/2014, 10:36:04 PM

Confirmations

6,242,528

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8883dd796bd020faabb68ec51d3ef10815fd86128ad173d1fc04c3259e9a2876
Transactions (2)
Coinbase6ceb1613362871…e519b66a79bc2f
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
0694d64b9359ed…8f3136cb9cc7ee
1 in β†’ 2 out6.2593 XPM226 B
AMWhfZow…EH5vsb34ARY5W8NX…Mn65UErP
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.

1.650 Γ— 10⁹⁷(98-digit number)
16506456600863366141…01864849357199534879
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.650 Γ— 10⁹⁷(98-digit number)
16506456600863366141…01864849357199534879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.301 Γ— 10⁹⁷(98-digit number)
33012913201726732283…03729698714399069759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.602 Γ— 10⁹⁷(98-digit number)
66025826403453464567…07459397428798139519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.320 Γ— 10⁹⁸(99-digit number)
13205165280690692913…14918794857596279039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.641 Γ— 10⁹⁸(99-digit number)
26410330561381385826…29837589715192558079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.282 Γ— 10⁹⁸(99-digit number)
52820661122762771653…59675179430385116159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.056 Γ— 10⁹⁹(100-digit number)
10564132224552554330…19350358860770232319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.112 Γ— 10⁹⁹(100-digit number)
21128264449105108661…38700717721540464639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.225 Γ— 10⁹⁹(100-digit number)
42256528898210217323…77401435443080929279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.451 Γ— 10⁹⁹(100-digit number)
84513057796420434646…54802870886161858559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.690 Γ— 10¹⁰⁰(101-digit number)
16902611559284086929…09605741772323717119
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,726,371 XPMΒ·at block #6,810,286 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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