XPM Prime Explorer symbol
XPMPrime Explorer

Block #621,374

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/7/2014, 10:09:21 AM Β· Difficulty 10.9519 Β· 6,174,888 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
985f72582e1a20fdf94376570ece86cf7ada950e0a730305eab01763598ae7d1
View on Chainz β†—

Height

#621,374

Difficulty

10.951893

Transactions

2

Size

547 B

Version

2

Bits

0af3af4a

Nonce

1,865,258,146

Timestamp

7/7/2014, 10:09:21 AM

Confirmations

6,174,888

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2e0739714f200982089e5f0c542ad2619dcada387486ea7dddecb944d2169600
Transactions (2)
Coinbasea36e7fe8bf1e1e…1a8559dcc95090
1 in β†’ 1 out8.3346 XPM116 B
ANSXnLY2…Sd25TjkD
741d4ea1c2915d…d43ca0ca5bf2f1
2 in β†’ 1 out3.0500 XPM340 B
ANeMs7aM…Fc9Pq5n2
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.

2.891 Γ— 10⁹⁢(97-digit number)
28919809041781178371…45185419294293996799
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
2.891 Γ— 10⁹⁢(97-digit number)
28919809041781178371…45185419294293996799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.783 Γ— 10⁹⁢(97-digit number)
57839618083562356742…90370838588587993599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.156 Γ— 10⁹⁷(98-digit number)
11567923616712471348…80741677177175987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.313 Γ— 10⁹⁷(98-digit number)
23135847233424942696…61483354354351974399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.627 Γ— 10⁹⁷(98-digit number)
46271694466849885393…22966708708703948799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.254 Γ— 10⁹⁷(98-digit number)
92543388933699770787…45933417417407897599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.850 Γ— 10⁹⁸(99-digit number)
18508677786739954157…91866834834815795199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.701 Γ— 10⁹⁸(99-digit number)
37017355573479908314…83733669669631590399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.403 Γ— 10⁹⁸(99-digit number)
74034711146959816629…67467339339263180799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.480 Γ— 10⁹⁹(100-digit number)
14806942229391963325…34934678678526361599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.961 Γ— 10⁹⁹(100-digit number)
29613884458783926651…69869357357052723199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,614,095 XPMΒ·at block #6,796,261 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