XPM Prime Explorer symbol
XPMPrime Explorer

Block #160,474

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2013, 11:12:50 PM Β· Difficulty 9.8608 Β· 6,638,037 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
66160ab0eb2b2efad663e6b3a0245bfed2d397588c453809998b42d3966dbd8c
View on Chainz β†—

Height

#160,474

Difficulty

9.860843

Transactions

1

Size

200 B

Version

2

Bits

09dc6038

Nonce

164,296

Timestamp

9/11/2013, 11:12:50 PM

Confirmations

6,638,037

Mined by

⛏️ P2SHAdPf23kymkynHU11focULiT8yrsAX3jtxK

Merkle Root

7105016aa453c89050990859b9af544e029cb9c081a2145e2f9db37830c96210
Transactions (1)
Coinbase7105016aa453c8…9db37830c96210
1 in β†’ 1 out10.2700 XPM109 B
AdPf23ky…sAX3jtxK
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.

1.006 Γ— 10⁹⁷(98-digit number)
10066617929131845628…08244527206204748801
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
1.006 Γ— 10⁹⁷(98-digit number)
10066617929131845628…08244527206204748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.013 Γ— 10⁹⁷(98-digit number)
20133235858263691257…16489054412409497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.026 Γ— 10⁹⁷(98-digit number)
40266471716527382515…32978108824818995201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.053 Γ— 10⁹⁷(98-digit number)
80532943433054765031…65956217649637990401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.610 Γ— 10⁹⁸(99-digit number)
16106588686610953006…31912435299275980801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.221 Γ— 10⁹⁸(99-digit number)
32213177373221906012…63824870598551961601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.442 Γ— 10⁹⁸(99-digit number)
64426354746443812024…27649741197103923201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.288 Γ— 10⁹⁹(100-digit number)
12885270949288762404…55299482394207846401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.577 Γ— 10⁹⁹(100-digit number)
25770541898577524809…10598964788415692801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,632,101 XPMΒ·at block #6,798,510 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