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Block #2,880,597

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2018, 9:56:57 AM Β· Difficulty 11.6329 Β· 3,963,441 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
55a589b308f50b7a0167ac9a4a27f1d9e5f519e7c197893707217365756907b7
View on Chainz β†—

Height

#2,880,597

Difficulty

11.632866

Transactions

2

Size

722 B

Version

2

Bits

0ba2037d

Nonce

1,286,090,240

Timestamp

10/14/2018, 9:56:57 AM

Confirmations

3,963,441

Mined by

⛏️ P2SHAXKrkFiYFG6CWUu3knVfBSWS58SXC4u97Q

Merkle Root

6c66a994213f22e7d73969540571f62c17be9e6f86f622c2b73a95484c3ba7c8
Transactions (2)
Coinbasecae9568ba6ae7c…32839df8cae433
1 in β†’ 1 out7.3900 XPM110 B
AXKrkFiY…SXC4u97Q
45d899ee5c9081…28ab562c9daa5e
3 in β†’ 2 out334.8351 XPM522 B
AaaYvziJ…y7UySFFUATreNT7b…d2xo2XhG
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.

4.264 Γ— 10⁹⁴(95-digit number)
42642159517263556122…30494415851879667519
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
4.264 Γ— 10⁹⁴(95-digit number)
42642159517263556122…30494415851879667519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.528 Γ— 10⁹⁴(95-digit number)
85284319034527112244…60988831703759335039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.705 Γ— 10⁹⁡(96-digit number)
17056863806905422448…21977663407518670079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.411 Γ— 10⁹⁡(96-digit number)
34113727613810844897…43955326815037340159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.822 Γ— 10⁹⁡(96-digit number)
68227455227621689795…87910653630074680319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.364 Γ— 10⁹⁢(97-digit number)
13645491045524337959…75821307260149360639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.729 Γ— 10⁹⁢(97-digit number)
27290982091048675918…51642614520298721279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.458 Γ— 10⁹⁢(97-digit number)
54581964182097351836…03285229040597442559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.091 Γ— 10⁹⁷(98-digit number)
10916392836419470367…06570458081194885119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.183 Γ— 10⁹⁷(98-digit number)
21832785672838940734…13140916162389770239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.366 Γ— 10⁹⁷(98-digit number)
43665571345677881469…26281832324779540479
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:57,996,682 XPMΒ·at block #6,844,037 Β· updates every 60s
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