XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,127,101

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/21/2017, 5:49:48 PM Β· Difficulty 10.9188 Β· 4,709,558 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
678075a9b5a34e866b6f82cef46da90a68138b44f37f8bb2c67083175d0ea630
View on Chainz β†—

Height

#2,127,101

Difficulty

10.918775

Transactions

3

Size

1.18 KB

Version

2

Bits

0aeb34d3

Nonce

17,300,479

Timestamp

5/21/2017, 5:49:48 PM

Confirmations

4,709,558

Mined by

⛏️ P2SHAUc6ty1mTJUeCpzbEoQBCP7pcUSFUkxJXh

Merkle Root

d8571b39aa196af1fdab10743865b85717be937173f4a02b0ef8d5b0bd328c98
Transactions (3)
Coinbase2ef85ae8cc6fc2…565ced535632d8
1 in β†’ 1 out8.3900 XPM110 B
AUc6ty1m…SFUkxJXh
1e94516831b690…86c5e62133e591
5 in β†’ 1 out999.9900 XPM786 B
AcxhUhX6…N8N8w2tm
ffbda3031d94df…7eaf4d8eabb7b6
1 in β†’ 2 out1653.4666 XPM227 B
AS3CFY4B…UF2wtmMRAVTkMg5T…4kNqt7rY
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.

2.294 Γ— 10⁹⁴(95-digit number)
22940274929849806283…29428639626948057039
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
2.294 Γ— 10⁹⁴(95-digit number)
22940274929849806283…29428639626948057039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.588 Γ— 10⁹⁴(95-digit number)
45880549859699612567…58857279253896114079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.176 Γ— 10⁹⁴(95-digit number)
91761099719399225134…17714558507792228159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.835 Γ— 10⁹⁡(96-digit number)
18352219943879845026…35429117015584456319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.670 Γ— 10⁹⁡(96-digit number)
36704439887759690053…70858234031168912639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.340 Γ— 10⁹⁡(96-digit number)
73408879775519380107…41716468062337825279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.468 Γ— 10⁹⁢(97-digit number)
14681775955103876021…83432936124675650559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.936 Γ— 10⁹⁢(97-digit number)
29363551910207752042…66865872249351301119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.872 Γ— 10⁹⁢(97-digit number)
58727103820415504085…33731744498702602239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.174 Γ— 10⁹⁷(98-digit number)
11745420764083100817…67463488997405204479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,937,549 XPMΒ·at block #6,836,658 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