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Block #3,132,036

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/9/2019, 5:35:06 PM Β· Difficulty 11.3101 Β· 3,701,859 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9674801a7d1b6586de594c8945807ade3a401757ea9f50580395130a12558464
View on Chainz β†—

Height

#3,132,036

Difficulty

11.310148

Transactions

2

Size

691 B

Version

2

Bits

0b4f65d6

Nonce

1,243,998,397

Timestamp

4/9/2019, 5:35:06 PM

Confirmations

3,701,859

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

a999137ac1a8bfb055101149dda2f24940ea5c7e9d6ef7f5ec997918e654e5f5
Transactions (2)
Coinbase407f8209ab0508…009e4d0e1dff3e
1 in β†’ 1 out7.8100 XPM110 B
AbXwmGxD…4XXYP765
94883d8b918f76…487b360c880a47
3 in β†’ 1 out997.9900 XPM491 B
AKxc3CpM…DNx7nkKS
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.

4.041 Γ— 10⁹⁴(95-digit number)
40417460368978665751…31134869600523200739
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
4.041 Γ— 10⁹⁴(95-digit number)
40417460368978665751…31134869600523200739
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.041 Γ— 10⁹⁴(95-digit number)
40417460368978665751…31134869600523200741
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
8.083 Γ— 10⁹⁴(95-digit number)
80834920737957331503…62269739201046401479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.083 Γ— 10⁹⁴(95-digit number)
80834920737957331503…62269739201046401481
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
1.616 Γ— 10⁹⁡(96-digit number)
16166984147591466300…24539478402092802959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.616 Γ— 10⁹⁡(96-digit number)
16166984147591466300…24539478402092802961
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
3.233 Γ— 10⁹⁡(96-digit number)
32333968295182932601…49078956804185605919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.233 Γ— 10⁹⁡(96-digit number)
32333968295182932601…49078956804185605921
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
6.466 Γ— 10⁹⁡(96-digit number)
64667936590365865202…98157913608371211839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.466 Γ— 10⁹⁡(96-digit number)
64667936590365865202…98157913608371211841
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
1.293 Γ— 10⁹⁢(97-digit number)
12933587318073173040…96315827216742423679
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:57,915,384 XPMΒ·at block #6,833,894 Β· updates every 60s
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