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Block #2,790,602

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/12/2018, 11:01:00 AM Β· Difficulty 11.6747 Β· 4,007,970 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
05c2ddb0efb57a9ce36ba5db26ba312315518d7e168d9d73e31843e88169eade
View on Chainz β†—

Height

#2,790,602

Difficulty

11.674741

Transactions

2

Size

504 B

Version

2

Bits

0bacbbcc

Nonce

608,248,625

Timestamp

8/12/2018, 11:01:00 AM

Confirmations

4,007,970

Mined by

⛏️ P2SHAQNwZw8MDMPg8FJu5SZQ6njHdQy27CbrF6

Merkle Root

9e37e2a23f6b0f5a78a7908ebc676c99dc30ec709096b6d0badeb01d808d0e39
Transactions (2)
Coinbasee67938b38cfd46…a3fc0e2f95987e
1 in β†’ 1 out7.3300 XPM109 B
AQNwZw8M…y27CbrF6
226776daa8b137…ce9b623070f588
2 in β†’ 2 out14.6300 XPM305 B
AKD9LeNP…bQTn8mEfAJHFSxQM…26L5oer4
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.

1.430 Γ— 10⁹⁴(95-digit number)
14308212721760081983…74566461980282602399
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.430 Γ— 10⁹⁴(95-digit number)
14308212721760081983…74566461980282602399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.430 Γ— 10⁹⁴(95-digit number)
14308212721760081983…74566461980282602401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.861 Γ— 10⁹⁴(95-digit number)
28616425443520163967…49132923960565204799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.861 Γ— 10⁹⁴(95-digit number)
28616425443520163967…49132923960565204801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.723 Γ— 10⁹⁴(95-digit number)
57232850887040327935…98265847921130409599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.723 Γ— 10⁹⁴(95-digit number)
57232850887040327935…98265847921130409601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.144 Γ— 10⁹⁡(96-digit number)
11446570177408065587…96531695842260819199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.144 Γ— 10⁹⁡(96-digit number)
11446570177408065587…96531695842260819201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.289 Γ— 10⁹⁡(96-digit number)
22893140354816131174…93063391684521638399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.289 Γ— 10⁹⁡(96-digit number)
22893140354816131174…93063391684521638401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.578 Γ— 10⁹⁡(96-digit number)
45786280709632262348…86126783369043276799
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,632,594 XPMΒ·at block #6,798,571 Β· updates every 60s
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