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Block #3,623,156

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/31/2020, 11:40:53 AM Β· Difficulty 10.9089 Β· 3,220,515 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bf84df6e4f8afd118fddd6fa8b34009f7f148c66d5d0e62c2c6ab41939aa0d76
View on Chainz β†—

Height

#3,623,156

Difficulty

10.908944

Transactions

1

Size

199 B

Version

2

Bits

0ae8b092

Nonce

1,609,829,761

Timestamp

3/31/2020, 11:40:53 AM

Confirmations

3,220,515

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

ae6e31970b584f0f65d774932081a5f644f6d1a648cd73491aae37512363a208
Transactions (1)
Coinbaseae6e31970b584f…ae37512363a208
1 in β†’ 1 out8.3900 XPM109 B
ASiq2qtK…VMhmk7yL
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.

9.067 Γ— 10⁹³(94-digit number)
90677640861063619512…45140089128700569199
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
9.067 Γ— 10⁹³(94-digit number)
90677640861063619512…45140089128700569199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.067 Γ— 10⁹³(94-digit number)
90677640861063619512…45140089128700569201
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
1.813 Γ— 10⁹⁴(95-digit number)
18135528172212723902…90280178257401138399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.813 Γ— 10⁹⁴(95-digit number)
18135528172212723902…90280178257401138401
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
3.627 Γ— 10⁹⁴(95-digit number)
36271056344425447805…80560356514802276799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.627 Γ— 10⁹⁴(95-digit number)
36271056344425447805…80560356514802276801
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
7.254 Γ— 10⁹⁴(95-digit number)
72542112688850895610…61120713029604553599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.254 Γ— 10⁹⁴(95-digit number)
72542112688850895610…61120713029604553601
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
1.450 Γ— 10⁹⁡(96-digit number)
14508422537770179122…22241426059209107199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.450 Γ— 10⁹⁡(96-digit number)
14508422537770179122…22241426059209107201
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:57,993,741 XPMΒ·at block #6,843,670 Β· updates every 60s
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