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Block #726,566

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/18/2014, 12:13:24 AM Β· Difficulty 10.9611 Β· 6,099,135 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
613af2b040202b14b53ddc99095fadca3466799054655b6255cc2452adef5050
View on Chainz β†—

Height

#726,566

Difficulty

10.961104

Transactions

2

Size

16.34 KB

Version

2

Bits

0af60aef

Nonce

1,098,390,031

Timestamp

9/18/2014, 12:13:24 AM

Confirmations

6,099,135

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

97ae5eb4c56d13392e39a3b91dfb0bb7ef3f320d52da470be3e292a88fb0f224
Transactions (2)
Coinbase6f07b8968cab0d…0ead033c87184c
1 in β†’ 1 out8.4800 XPM116 B
ANSXnLY2…Sd25TjkD
1d8df7a83dbf25…3746540785f855
112 in β†’ 2 out900.0100 XPM16.13 KB
AdvurNjz…j1oXi361ATFJP83H…qtZtW8QR
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.

3.707 Γ— 10⁹⁢(97-digit number)
37073763719343900474…91913035062246256639
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
3.707 Γ— 10⁹⁢(97-digit number)
37073763719343900474…91913035062246256639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.414 Γ— 10⁹⁢(97-digit number)
74147527438687800948…83826070124492513279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.482 Γ— 10⁹⁷(98-digit number)
14829505487737560189…67652140248985026559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.965 Γ— 10⁹⁷(98-digit number)
29659010975475120379…35304280497970053119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.931 Γ— 10⁹⁷(98-digit number)
59318021950950240758…70608560995940106239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.186 Γ— 10⁹⁸(99-digit number)
11863604390190048151…41217121991880212479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.372 Γ— 10⁹⁸(99-digit number)
23727208780380096303…82434243983760424959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.745 Γ— 10⁹⁸(99-digit number)
47454417560760192607…64868487967520849919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.490 Γ— 10⁹⁸(99-digit number)
94908835121520385214…29736975935041699839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.898 Γ— 10⁹⁹(100-digit number)
18981767024304077042…59473951870083399679
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,849,719 XPMΒ·at block #6,825,700 Β· updates every 60s
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