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Block #3,632,864

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/7/2020, 10:05:23 AM Β· Difficulty 10.9042 Β· 3,208,436 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
caa988d2b56c565b8d6ecb1469569adab6509eb1b1be903cc8654f865ca1670c
View on Chainz β†—

Height

#3,632,864

Difficulty

10.904177

Transactions

2

Size

723 B

Version

2

Bits

0ae7781f

Nonce

1,727,090,773

Timestamp

4/7/2020, 10:05:23 AM

Confirmations

3,208,436

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

945a231e312b79e8c7b9047747449b7f83d6e01dfeda966a4ec1b833bec7004b
Transactions (2)
Coinbase52e91ae86a7524…16652695dbdf2d
1 in β†’ 1 out8.5000 XPM110 B
ASiq2qtK…VMhmk7yL
18ef583cf26fd6…2ceafd710e5894
3 in β†’ 2 out8548.1528 XPM522 B
AX3W6pJy…NwZ88svUAFnhfyw9…AyM5Lz6f
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.

6.314 Γ— 10⁹⁷(98-digit number)
63141229658842105943…73671033070561198079
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
6.314 Γ— 10⁹⁷(98-digit number)
63141229658842105943…73671033070561198079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.314 Γ— 10⁹⁷(98-digit number)
63141229658842105943…73671033070561198081
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
1.262 Γ— 10⁹⁸(99-digit number)
12628245931768421188…47342066141122396159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.262 Γ— 10⁹⁸(99-digit number)
12628245931768421188…47342066141122396161
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
2.525 Γ— 10⁹⁸(99-digit number)
25256491863536842377…94684132282244792319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.525 Γ— 10⁹⁸(99-digit number)
25256491863536842377…94684132282244792321
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
5.051 Γ— 10⁹⁸(99-digit number)
50512983727073684755…89368264564489584639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.051 Γ— 10⁹⁸(99-digit number)
50512983727073684755…89368264564489584641
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
1.010 Γ— 10⁹⁹(100-digit number)
10102596745414736951…78736529128979169279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.010 Γ— 10⁹⁹(100-digit number)
10102596745414736951…78736529128979169281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
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 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:57,974,767 XPMΒ·at block #6,841,299 Β· updates every 60s
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