XPM Prime Explorer symbol
XPMPrime Explorer

Block #39,641

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 1:48:10 PM Β· Difficulty 8.3435 Β· 6,757,260 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0576891c87fb64d5e37956f0ea824f32c3ed8b0cbe92dda0f372ce2179398ccb
View on Chainz β†—

Height

#39,641

Difficulty

8.343458

Transactions

1

Size

204 B

Version

2

Bits

0857ecdf

Nonce

0

Timestamp

7/14/2013, 1:48:10 PM

Confirmations

6,757,260

Mined by

⛏️ P2SHAVzQ3NvcgEu72cQUAUtfvzgK4M3tozGjpc

Merkle Root

2ba22e8a43d20b40b15905069595866017ed55d2c97125d91a78c173fdf451e7
Transactions (1)
Coinbase2ba22e8a43d20b…78c173fdf451e7
1 in β†’ 1 out14.3500 XPM110 B
AVzQ3Nvc…3tozGjpc
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.

1.098 Γ— 10¹⁰⁡(106-digit number)
10989394039465731293…48571340040278320679
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
1.098 Γ— 10¹⁰⁡(106-digit number)
10989394039465731293…48571340040278320679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.197 Γ— 10¹⁰⁡(106-digit number)
21978788078931462586…97142680080556641359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.395 Γ— 10¹⁰⁡(106-digit number)
43957576157862925173…94285360161113282719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.791 Γ— 10¹⁰⁡(106-digit number)
87915152315725850347…88570720322226565439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.758 Γ— 10¹⁰⁢(107-digit number)
17583030463145170069…77141440644453130879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.516 Γ— 10¹⁰⁢(107-digit number)
35166060926290340139…54282881288906261759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.033 Γ— 10¹⁰⁢(107-digit number)
70332121852580680278…08565762577812523519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.406 Γ— 10¹⁰⁷(108-digit number)
14066424370516136055…17131525155625047039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,619,228 XPMΒ·at block #6,796,900 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK