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Block #2,585,653

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/25/2018, 11:06:42 PM Β· Difficulty 11.2564 Β· 4,245,394 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea790c69eac4f9809789dc4f99fcf302bfe36e5ab6dcf6bd93947e779adac644
View on Chainz β†—

Height

#2,585,653

Difficulty

11.256416

Transactions

2

Size

689 B

Version

2

Bits

0b41a483

Nonce

657,588,616

Timestamp

3/25/2018, 11:06:42 PM

Confirmations

4,245,394

Mined by

⛏️ P2SHALPqe5Svv4EvMT9NQEwLHpENwQAzcQRGVX

Merkle Root

645f12d95c2c17142e7e48222f86589b9102bfcb958d25c90e804eeec9e0c4b3
Transactions (2)
Coinbase539d69a7786b17…6a84e2139b4d1b
1 in β†’ 1 out7.8900 XPM110 B
ALPqe5Sv…AzcQRGVX
f2c37f65937bcc…52428b71d9416b
3 in β†’ 1 out11.9900 XPM490 B
ASEhqc6y…uiLW8tms
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.

1.823 Γ— 10⁹³(94-digit number)
18231981960041752578…49062567712409860459
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
1.823 Γ— 10⁹³(94-digit number)
18231981960041752578…49062567712409860459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.646 Γ— 10⁹³(94-digit number)
36463963920083505156…98125135424819720919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.292 Γ— 10⁹³(94-digit number)
72927927840167010313…96250270849639441839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.458 Γ— 10⁹⁴(95-digit number)
14585585568033402062…92500541699278883679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.917 Γ— 10⁹⁴(95-digit number)
29171171136066804125…85001083398557767359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.834 Γ— 10⁹⁴(95-digit number)
58342342272133608250…70002166797115534719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.166 Γ— 10⁹⁡(96-digit number)
11668468454426721650…40004333594231069439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.333 Γ— 10⁹⁡(96-digit number)
23336936908853443300…80008667188462138879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.667 Γ— 10⁹⁡(96-digit number)
46673873817706886600…60017334376924277759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.334 Γ— 10⁹⁡(96-digit number)
93347747635413773201…20034668753848555519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.866 Γ— 10⁹⁢(97-digit number)
18669549527082754640…40069337507697111039
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:57,892,512 XPMΒ·at block #6,831,046 Β· updates every 60s
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