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Block #2,116,474

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/14/2017, 10:21:01 PM Β· Difficulty 10.9041 Β· 4,725,287 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
199cedcce6c15fde4303b80ac6fb9623bc5db3af8c829a4f5ac5a3ab0836c31b
View on Chainz β†—

Height

#2,116,474

Difficulty

10.904075

Transactions

1

Size

243 B

Version

2

Bits

0ae77178

Nonce

2,300,231,976

Timestamp

5/14/2017, 10:21:01 PM

Confirmations

4,725,287

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

0a88e83cf8a68ca67a880ceeef65a43ad8cdc66c246d0b9d3bd565d5d434d382
Transactions (1)
Coinbase0a88e83cf8a68c…d565d5d434d382
1 in β†’ 2 out8.4000 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

3.101 Γ— 10⁹⁢(97-digit number)
31019215446017911699…14058597637239368959
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
3.101 Γ— 10⁹⁢(97-digit number)
31019215446017911699…14058597637239368959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.101 Γ— 10⁹⁢(97-digit number)
31019215446017911699…14058597637239368961
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
6.203 Γ— 10⁹⁢(97-digit number)
62038430892035823399…28117195274478737919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.203 Γ— 10⁹⁢(97-digit number)
62038430892035823399…28117195274478737921
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
1.240 Γ— 10⁹⁷(98-digit number)
12407686178407164679…56234390548957475839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.240 Γ— 10⁹⁷(98-digit number)
12407686178407164679…56234390548957475841
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
2.481 Γ— 10⁹⁷(98-digit number)
24815372356814329359…12468781097914951679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.481 Γ— 10⁹⁷(98-digit number)
24815372356814329359…12468781097914951681
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
4.963 Γ— 10⁹⁷(98-digit number)
49630744713628658719…24937562195829903359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.963 Γ— 10⁹⁷(98-digit number)
49630744713628658719…24937562195829903361
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
9.926 Γ— 10⁹⁷(98-digit number)
99261489427257317439…49875124391659806719
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
Circulating Supply:57,978,462 XPMΒ·at block #6,841,760 Β· updates every 60s
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