XPM Prime Explorer symbol
XPMPrime Explorer

Block #89,807

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/30/2013, 3:39:28 PM Β· Difficulty 9.2542 Β· 6,705,241 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
78e9eae3ce75fa895eea221f99ebb2b211e1c5becfdb1f790078506b227e730e
View on Chainz β†—

Height

#89,807

Difficulty

9.254173

Transactions

1

Size

200 B

Version

2

Bits

0941117a

Nonce

590,325

Timestamp

7/30/2013, 3:39:28 PM

Confirmations

6,705,241

Mined by

⛏️ P2SHAWuDuxGXKEXYj7RYhx64EdJKzBtLDpHWp7

Merkle Root

786d706bf8a0b7b06bc16131e99824d99d32b7b16b146eca6c24e48a7df6f324
Transactions (1)
Coinbase786d706bf8a0b7…24e48a7df6f324
1 in β†’ 1 out11.6600 XPM109 B
AWuDuxGX…tLDpHWp7
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.

1.517 Γ— 10⁹⁢(97-digit number)
15170570398975051167…53737124931238814789
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
1.517 Γ— 10⁹⁢(97-digit number)
15170570398975051167…53737124931238814789
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.034 Γ— 10⁹⁢(97-digit number)
30341140797950102334…07474249862477629579
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.068 Γ— 10⁹⁢(97-digit number)
60682281595900204669…14948499724955259159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.213 Γ— 10⁹⁷(98-digit number)
12136456319180040933…29896999449910518319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.427 Γ— 10⁹⁷(98-digit number)
24272912638360081867…59793998899821036639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.854 Γ— 10⁹⁷(98-digit number)
48545825276720163735…19587997799642073279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.709 Γ— 10⁹⁷(98-digit number)
97091650553440327471…39175995599284146559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.941 Γ— 10⁹⁸(99-digit number)
19418330110688065494…78351991198568293119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.883 Γ— 10⁹⁸(99-digit number)
38836660221376130988…56703982397136586239
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 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 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,604,424 XPMΒ·at block #6,795,047 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