XPM Prime Explorer symbol
XPMPrime Explorer

Block #72,357

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 11:38:11 PM Β· Difficulty 8.9940 Β· 6,727,127 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9bfc9be6d4dd74a414b5f0a4218251c38534141ca7515324a62eec312801385c
View on Chainz β†—

Height

#72,357

Difficulty

8.994006

Transactions

1

Size

200 B

Version

2

Bits

08fe7732

Nonce

199

Timestamp

7/20/2013, 11:38:11 PM

Confirmations

6,727,127

Mined by

⛏️ P2SHANCYL9xhLGasWxPCKGNNvToMvF9WyGnqDE

Merkle Root

e0200fd9455991d3a81474150387a600b79d86b513d1a58701b255aac23a2f04
Transactions (1)
Coinbasee0200fd9455991…b255aac23a2f04
1 in β†’ 1 out12.3400 XPM110 B
ANCYL9xh…9WyGnqDE
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.

8.597 Γ— 10⁹⁴(95-digit number)
85975085996058308157…09454530009113313629
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
8.597 Γ— 10⁹⁴(95-digit number)
85975085996058308157…09454530009113313629
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁡(96-digit number)
17195017199211661631…18909060018226627259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.439 Γ— 10⁹⁡(96-digit number)
34390034398423323263…37818120036453254519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.878 Γ— 10⁹⁡(96-digit number)
68780068796846646526…75636240072906509039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.375 Γ— 10⁹⁢(97-digit number)
13756013759369329305…51272480145813018079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.751 Γ— 10⁹⁢(97-digit number)
27512027518738658610…02544960291626036159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.502 Γ— 10⁹⁢(97-digit number)
55024055037477317220…05089920583252072319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.100 Γ— 10⁹⁷(98-digit number)
11004811007495463444…10179841166504144639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.200 Γ— 10⁹⁷(98-digit number)
22009622014990926888…20359682333008289279
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:57,639,914 XPMΒ·at block #6,799,483 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