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Block #1,565,439

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2016, 5:57:45 AM Β· Difficulty 10.7536 Β· 5,248,786 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9fce47e403c06af332c630427a59d57725f5ea45c98a20287474a9cd996e5fd0
View on Chainz β†—

Height

#1,565,439

Difficulty

10.753607

Transactions

1

Size

199 B

Version

2

Bits

0ac0ec62

Nonce

1,365,427,785

Timestamp

4/30/2016, 5:57:45 AM

Confirmations

5,248,786

Mined by

⛏️ P2SHAGeKusvpLiop1Tt88BzehBSnv7weaMkB7t

Merkle Root

3b02daba0e02ebb10e87f01d8d6eff456abb7f0801f10252af7e2f8a40c0b80e
Transactions (1)
Coinbase3b02daba0e02eb…7e2f8a40c0b80e
1 in β†’ 1 out8.6300 XPM109 B
AGeKusvp…weaMkB7t
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.

4.601 Γ— 10⁹³(94-digit number)
46016561318636774870…92526129065183847999
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
4.601 Γ— 10⁹³(94-digit number)
46016561318636774870…92526129065183847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.203 Γ— 10⁹³(94-digit number)
92033122637273549740…85052258130367695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.840 Γ— 10⁹⁴(95-digit number)
18406624527454709948…70104516260735391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.681 Γ— 10⁹⁴(95-digit number)
36813249054909419896…40209032521470783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.362 Γ— 10⁹⁴(95-digit number)
73626498109818839792…80418065042941567999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.472 Γ— 10⁹⁡(96-digit number)
14725299621963767958…60836130085883135999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.945 Γ— 10⁹⁡(96-digit number)
29450599243927535916…21672260171766271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.890 Γ— 10⁹⁡(96-digit number)
58901198487855071833…43344520343532543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.178 Γ— 10⁹⁢(97-digit number)
11780239697571014366…86689040687065087999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.356 Γ— 10⁹⁢(97-digit number)
23560479395142028733…73378081374130175999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.712 Γ— 10⁹⁢(97-digit number)
47120958790284057466…46756162748260351999
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:57,757,870 XPMΒ·at block #6,814,224 Β· updates every 60s
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