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Block #1,303,974

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/29/2015, 4:54:46 PM Β· Difficulty 10.8534 Β· 5,513,196 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9a9771705b35bb8fbfea7931d18798b2951dc777af89f22a13b63c1458dcc539
View on Chainz β†—

Height

#1,303,974

Difficulty

10.853385

Transactions

2

Size

2.88 KB

Version

2

Bits

0ada7770

Nonce

330,008,229

Timestamp

10/29/2015, 4:54:46 PM

Confirmations

5,513,196

Mined by

⛏️ P2SHAJKFb4Tkp6dUy5Ng2PVE1Z88Eacm2ssaiG

Merkle Root

8bdaa2ed31b30bc89680ee24d7e8935b193d8f8353fc9836be84e3042e722f1c
Transactions (2)
Coinbase8518369c98a013…265c0e0d5288e6
1 in β†’ 1 out8.5100 XPM110 B
AJKFb4Tk…cm2ssaiG
138cbbae069db5…1765f73e4c4614
18 in β†’ 2 out2749.7216 XPM2.68 KB
ANokhJ91…ugeUHh6tAQ8obrRF…hCezsXdr
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.

3.637 Γ— 10⁹⁴(95-digit number)
36370483457620284012…35902675442683271439
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
3.637 Γ— 10⁹⁴(95-digit number)
36370483457620284012…35902675442683271439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.274 Γ— 10⁹⁴(95-digit number)
72740966915240568025…71805350885366542879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.454 Γ— 10⁹⁡(96-digit number)
14548193383048113605…43610701770733085759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.909 Γ— 10⁹⁡(96-digit number)
29096386766096227210…87221403541466171519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.819 Γ— 10⁹⁡(96-digit number)
58192773532192454420…74442807082932343039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.163 Γ— 10⁹⁢(97-digit number)
11638554706438490884…48885614165864686079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.327 Γ— 10⁹⁢(97-digit number)
23277109412876981768…97771228331729372159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.655 Γ— 10⁹⁢(97-digit number)
46554218825753963536…95542456663458744319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.310 Γ— 10⁹⁢(97-digit number)
93108437651507927072…91084913326917488639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.862 Γ— 10⁹⁷(98-digit number)
18621687530301585414…82169826653834977279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.724 Γ— 10⁹⁷(98-digit number)
37243375060603170828…64339653307669954559
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:57,781,395 XPMΒ·at block #6,817,169 Β· updates every 60s
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