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Block #2,913,169

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/7/2018, 3:14:09 AM Β· Difficulty 11.4986 Β· 3,920,204 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
57938e0436dafe9f4870f3e7167c404a9e1717590053f0b91e7360af64b1ea5e
View on Chainz β†—

Height

#2,913,169

Difficulty

11.498621

Transactions

2

Size

1.57 KB

Version

2

Bits

0b7fa59f

Nonce

735,230,652

Timestamp

11/7/2018, 3:14:09 AM

Confirmations

3,920,204

Mined by

⛏️ P2SHAPio4RL3Vyt2jyLuVemx6qBNZJrgMP3gGn

Merkle Root

6abbe23fb4037e9b0f33881ac4f796d7fd6b1d3e7146c97d819dc684f66795f7
Transactions (2)
Coinbase01c331e978a3e3…9152370ecfc602
1 in β†’ 1 out7.5700 XPM110 B
APio4RL3…rgMP3gGn
1885d87060d6d7…edadc08f9bd098
9 in β†’ 2 out178.7013 XPM1.38 KB
AYKEixAt…qG9KZfGhAYNGhdg5…y5SCmaE1
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.

1.505 Γ— 10⁹⁢(97-digit number)
15050098467184273680…15872040857413877759
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
1.505 Γ— 10⁹⁢(97-digit number)
15050098467184273680…15872040857413877759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.505 Γ— 10⁹⁢(97-digit number)
15050098467184273680…15872040857413877761
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
3.010 Γ— 10⁹⁢(97-digit number)
30100196934368547361…31744081714827755519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.010 Γ— 10⁹⁢(97-digit number)
30100196934368547361…31744081714827755521
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
6.020 Γ— 10⁹⁢(97-digit number)
60200393868737094722…63488163429655511039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.020 Γ— 10⁹⁢(97-digit number)
60200393868737094722…63488163429655511041
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
1.204 Γ— 10⁹⁷(98-digit number)
12040078773747418944…26976326859311022079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.204 Γ— 10⁹⁷(98-digit number)
12040078773747418944…26976326859311022081
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
2.408 Γ— 10⁹⁷(98-digit number)
24080157547494837889…53952653718622044159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.408 Γ— 10⁹⁷(98-digit number)
24080157547494837889…53952653718622044161
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
4.816 Γ— 10⁹⁷(98-digit number)
48160315094989675778…07905307437244088319
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
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