XPM Prime Explorer symbol
XPMPrime Explorer

Block #840,916

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2014, 11:59:57 AM Β· Difficulty 10.9742 Β· 6,002,412 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
11c71e045aaa0f94ed207575d4b41ec067d1d3bb2b2d2605c024641df934be38
View on Chainz β†—

Height

#840,916

Difficulty

10.974239

Transactions

2

Size

431 B

Version

2

Bits

0af967bc

Nonce

327,238,658

Timestamp

12/5/2014, 11:59:57 AM

Confirmations

6,002,412

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c91baac265737db3b6c608df5bca36262d48a7dd3447d5171199ff6a3e9acdd0
Transactions (2)
Coinbase070823c292ea4c…d8a5c96b40f0b2
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
0e12099832691a…6859019b486ada
1 in β†’ 2 out0.3148 XPM225 B
Af3Xcs3M…rkD1QeQcAKB46hq1…HFkcQprx
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.

2.002 Γ— 10⁹⁴(95-digit number)
20023107112508650673…00139652865565513749
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
2.002 Γ— 10⁹⁴(95-digit number)
20023107112508650673…00139652865565513749
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.004 Γ— 10⁹⁴(95-digit number)
40046214225017301347…00279305731131027499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.009 Γ— 10⁹⁴(95-digit number)
80092428450034602695…00558611462262054999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.601 Γ— 10⁹⁡(96-digit number)
16018485690006920539…01117222924524109999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.203 Γ— 10⁹⁡(96-digit number)
32036971380013841078…02234445849048219999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.407 Γ— 10⁹⁡(96-digit number)
64073942760027682156…04468891698096439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.281 Γ— 10⁹⁢(97-digit number)
12814788552005536431…08937783396192879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.562 Γ— 10⁹⁢(97-digit number)
25629577104011072862…17875566792385759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.125 Γ— 10⁹⁢(97-digit number)
51259154208022145725…35751133584771519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.025 Γ— 10⁹⁷(98-digit number)
10251830841604429145…71502267169543039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.050 Γ— 10⁹⁷(98-digit number)
20503661683208858290…43004534339086079999
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:57,990,985 XPMΒ·at block #6,843,327 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.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy