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Block #2,095,544

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2017, 9:26:05 AM Β· Difficulty 10.8717 Β· 4,735,694 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4c491f0bdd4712b951bce3a2295620d25fcebce97f82e43b849c73b6b7654951
View on Chainz β†—

Height

#2,095,544

Difficulty

10.871700

Transactions

2

Size

1.68 KB

Version

2

Bits

0adf27b8

Nonce

817,157,309

Timestamp

5/1/2017, 9:26:05 AM

Confirmations

4,735,694

Mined by

⛏️ P2SHAHF5ssGxKqaTjaTQSgxU4SSmXM3j2tzFTs

Merkle Root

773e6e39fcd797af2d82828df4608244c1f82460a0ccfabf7ad6cd103f915c5e
Transactions (2)
Coinbasefebfe5bcbdda3a…a259d48da88abf
1 in β†’ 1 out8.4700 XPM109 B
AHF5ssGx…3j2tzFTs
da3c267b25a4c0…9f384fdd2ab417
10 in β†’ 1 out2442.9586 XPM1.49 KB
AYoy228q…feZqXfNq
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.

7.698 Γ— 10⁹³(94-digit number)
76989732374404364900…59977008343080810699
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
7.698 Γ— 10⁹³(94-digit number)
76989732374404364900…59977008343080810699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.698 Γ— 10⁹³(94-digit number)
76989732374404364900…59977008343080810701
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
1.539 Γ— 10⁹⁴(95-digit number)
15397946474880872980…19954016686161621399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.539 Γ— 10⁹⁴(95-digit number)
15397946474880872980…19954016686161621401
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
3.079 Γ— 10⁹⁴(95-digit number)
30795892949761745960…39908033372323242799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.079 Γ— 10⁹⁴(95-digit number)
30795892949761745960…39908033372323242801
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
6.159 Γ— 10⁹⁴(95-digit number)
61591785899523491920…79816066744646485599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.159 Γ— 10⁹⁴(95-digit number)
61591785899523491920…79816066744646485601
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
1.231 Γ— 10⁹⁡(96-digit number)
12318357179904698384…59632133489292971199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.231 Γ— 10⁹⁡(96-digit number)
12318357179904698384…59632133489292971201
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:57,894,053 XPMΒ·at block #6,831,237 Β· updates every 60s
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