XPM Prime Explorer symbol
XPMPrime Explorer

Block #158,927

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2013, 6:21:07 PM Β· Difficulty 9.8657 Β· 6,646,118 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09c0c2978f89e8001f40a6fb46848d1c2f2e6dc098f2b40688c0d858d54ccc1a
View on Chainz β†—

Height

#158,927

Difficulty

9.865733

Transactions

9

Size

6.44 KB

Version

2

Bits

09dda0af

Nonce

70,579

Timestamp

9/10/2013, 6:21:07 PM

Confirmations

6,646,118

Mined by

⛏️ P2SHAZ6tNwWZXsoZL2aaGQ4KANbxFRsY8faWM4

Merkle Root

ec019b98e92d0f38f4003b58c1f6edf647f0736e4799c583710ba2413682babd
Transactions (9)
Coinbasebbd16c64b205ea…99c7d44a3d3462
1 in β†’ 1 out10.3900 XPM109 B
AZ6tNwWZ…sY8faWM4
dde837750256e2…37e2cd61c14324
1 in β†’ 1 out10.2600 XPM158 B
AS3dWkP6…9YgFYgqQ
9e16ded5150948…5238dbe7cd30ec
1 in β†’ 1 out10.2600 XPM158 B
AS3dWkP6…9YgFYgqQ
325ff46214c127…823f75a57ab5e1
1 in β†’ 1 out10.2500 XPM157 B
AS3dWkP6…9YgFYgqQ
404604e22a980c…f0552d97719487
46 in β†’ 1 out472.2000 XPM5.17 KB
AYeYSNLo…NiL9hDLh
44b33ade6a36a5…a0c8179274acb9
1 in β†’ 1 out10.2500 XPM158 B
AS3dWkP6…9YgFYgqQ
837bb6f28b7aa0…09b98234e90646
1 in β†’ 1 out10.2500 XPM157 B
AS3dWkP6…9YgFYgqQ
cc66da5c88d7ab…7ffbf85a4ebc64
1 in β†’ 1 out10.2600 XPM158 B
AS3dWkP6…9YgFYgqQ
421ca18264a7f8…08dbb1d8ee1f1d
1 in β†’ 1 out10.2600 XPM157 B
AS3dWkP6…9YgFYgqQ
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.

6.692 Γ— 10⁹³(94-digit number)
66922186391911467749…09924259838687321241
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.692 Γ— 10⁹³(94-digit number)
66922186391911467749…09924259838687321241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.338 Γ— 10⁹⁴(95-digit number)
13384437278382293549…19848519677374642481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.676 Γ— 10⁹⁴(95-digit number)
26768874556764587099…39697039354749284961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.353 Γ— 10⁹⁴(95-digit number)
53537749113529174199…79394078709498569921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.070 Γ— 10⁹⁡(96-digit number)
10707549822705834839…58788157418997139841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.141 Γ— 10⁹⁡(96-digit number)
21415099645411669679…17576314837994279681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.283 Γ— 10⁹⁡(96-digit number)
42830199290823339359…35152629675988559361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.566 Γ— 10⁹⁡(96-digit number)
85660398581646678719…70305259351977118721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.713 Γ— 10⁹⁢(97-digit number)
17132079716329335743…40610518703954237441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.426 Γ— 10⁹⁢(97-digit number)
34264159432658671487…81221037407908474881
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,684,425 XPMΒ·at block #6,805,044 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