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Block #2,139,011

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2017, 9:19:57 AM Β· Difficulty 10.8801 Β· 4,699,936 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51b6853b44790e11153dfedd441e4ba980269ce86bd433a8511073b3ebbd030f
View on Chainz β†—

Height

#2,139,011

Difficulty

10.880114

Transactions

1

Size

200 B

Version

2

Bits

0ae14f23

Nonce

321,776,162

Timestamp

5/31/2017, 9:19:57 AM

Confirmations

4,699,936

Mined by

⛏️ P2SHAJLUYPFQKEyzh9BNeQzxozsgqr1DcTChV4

Merkle Root

7f27126e981b866443ef8e129da531e71169865ecbe0afe666645457f74308b3
Transactions (1)
Coinbase7f27126e981b86…645457f74308b3
1 in β†’ 1 out8.4300 XPM109 B
AJLUYPFQ…1DcTChV4
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.

1.450 Γ— 10⁹⁢(97-digit number)
14506192958250473224…60612856763925565439
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
1.450 Γ— 10⁹⁢(97-digit number)
14506192958250473224…60612856763925565439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.901 Γ— 10⁹⁢(97-digit number)
29012385916500946448…21225713527851130879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.802 Γ— 10⁹⁢(97-digit number)
58024771833001892896…42451427055702261759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.160 Γ— 10⁹⁷(98-digit number)
11604954366600378579…84902854111404523519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.320 Γ— 10⁹⁷(98-digit number)
23209908733200757158…69805708222809047039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.641 Γ— 10⁹⁷(98-digit number)
46419817466401514317…39611416445618094079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.283 Γ— 10⁹⁷(98-digit number)
92839634932803028634…79222832891236188159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.856 Γ— 10⁹⁸(99-digit number)
18567926986560605726…58445665782472376319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.713 Γ— 10⁹⁸(99-digit number)
37135853973121211453…16891331564944752639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.427 Γ— 10⁹⁸(99-digit number)
74271707946242422907…33782663129889505279
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:57,955,842 XPMΒ·at block #6,838,946 Β· updates every 60s
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