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Block #3,160,165

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/29/2019, 6:33:55 AM Β· Difficulty 11.3100 Β· 3,681,500 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7b8c1275a2dce60292a2426400015ae22511cbcef0ede1ea98c57011dce4780d
View on Chainz β†—

Height

#3,160,165

Difficulty

11.310019

Transactions

1

Size

201 B

Version

2

Bits

0b4f5d64

Nonce

1,639,719,025

Timestamp

4/29/2019, 6:33:55 AM

Confirmations

3,681,500

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

8a89973890d6bc807f416d5ce2332e8e69d75d075b27a46eb9c28600ffaadc07
Transactions (1)
Coinbase8a89973890d6bc…c28600ffaadc07
1 in β†’ 1 out7.8000 XPM110 B
AbXwmGxD…4XXYP765
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.

2.729 Γ— 10⁹⁢(97-digit number)
27299723643298616797…14343420537090248959
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
2.729 Γ— 10⁹⁢(97-digit number)
27299723643298616797…14343420537090248959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.729 Γ— 10⁹⁢(97-digit number)
27299723643298616797…14343420537090248961
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
5.459 Γ— 10⁹⁢(97-digit number)
54599447286597233594…28686841074180497919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.459 Γ— 10⁹⁢(97-digit number)
54599447286597233594…28686841074180497921
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
1.091 Γ— 10⁹⁷(98-digit number)
10919889457319446718…57373682148360995839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.091 Γ— 10⁹⁷(98-digit number)
10919889457319446718…57373682148360995841
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
2.183 Γ— 10⁹⁷(98-digit number)
21839778914638893437…14747364296721991679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.183 Γ— 10⁹⁷(98-digit number)
21839778914638893437…14747364296721991681
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
4.367 Γ— 10⁹⁷(98-digit number)
43679557829277786875…29494728593443983359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.367 Γ— 10⁹⁷(98-digit number)
43679557829277786875…29494728593443983361
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
8.735 Γ— 10⁹⁷(98-digit number)
87359115658555573751…58989457186887966719
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
8.735 Γ— 10⁹⁷(98-digit number)
87359115658555573751…58989457186887966721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,977,709 XPMΒ·at block #6,841,664 Β· updates every 60s
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