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Block #2,632,836

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 2:13:22 AM Β· Difficulty 11.1772 Β· 4,211,583 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
38727ef754d90c8fedd691c2c7d0a506216435ba2200a74dd2310d2e13812166
View on Chainz β†—

Height

#2,632,836

Difficulty

11.177168

Transactions

2

Size

575 B

Version

2

Bits

0b2d5ae5

Nonce

834,306,537

Timestamp

4/28/2018, 2:13:22 AM

Confirmations

4,211,583

Mined by

⛏️ P2SHARQDji1YpaQA8Hnt7qu8B3iJJPCzCAa71o

Merkle Root

1d64da0b836e238479afaf05afe437a7b2e1084588d55f0ce52b0d9534ebe66f
Transactions (2)
Coinbasec902296a594611…1ee8a2a2325131
1 in β†’ 1 out8.0100 XPM110 B
ARQDji1Y…CzCAa71o
a23102993f5894…564e2338d4051e
2 in β†’ 2 out331.6278 XPM375 B
AQWa8gAp…JqSGS3Q9AHJeiJjZ…AtVjQXra
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.

1.156 Γ— 10⁹⁴(95-digit number)
11569174729665297773…90296989433414348799
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
1.156 Γ— 10⁹⁴(95-digit number)
11569174729665297773…90296989433414348799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.156 Γ— 10⁹⁴(95-digit number)
11569174729665297773…90296989433414348801
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
2.313 Γ— 10⁹⁴(95-digit number)
23138349459330595547…80593978866828697599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.313 Γ— 10⁹⁴(95-digit number)
23138349459330595547…80593978866828697601
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
4.627 Γ— 10⁹⁴(95-digit number)
46276698918661191094…61187957733657395199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.627 Γ— 10⁹⁴(95-digit number)
46276698918661191094…61187957733657395201
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
9.255 Γ— 10⁹⁴(95-digit number)
92553397837322382188…22375915467314790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.255 Γ— 10⁹⁴(95-digit number)
92553397837322382188…22375915467314790401
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
1.851 Γ— 10⁹⁡(96-digit number)
18510679567464476437…44751830934629580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.851 Γ— 10⁹⁡(96-digit number)
18510679567464476437…44751830934629580801
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
3.702 Γ— 10⁹⁡(96-digit number)
37021359134928952875…89503661869259161599
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:57,999,747 XPMΒ·at block #6,844,418 Β· updates every 60s
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