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Block #3,240,509

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2019, 3:36:22 PM Β· Difficulty 11.0029 Β· 3,577,429 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fc00b646cfa0ae64bbaac866295872ea7f7bd0cc8fe9cd174e32866e3f567f92
View on Chainz β†—

Height

#3,240,509

Difficulty

11.002894

Transactions

2

Size

872 B

Version

2

Bits

0b00bda2

Nonce

128,357,184

Timestamp

6/25/2019, 3:36:22 PM

Confirmations

3,577,429

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

d42c177c87171f07dd55f575e19bd56292a877c3cfa263548a4912e2190f849f
Transactions (2)
Coinbase5822977234940b…f7f916ae25ef8b
1 in β†’ 1 out8.2600 XPM110 B
ARbm48qR…9xQc8DBX
b828d946950381…cebb557d22f537
4 in β†’ 2 out69.6871 XPM671 B
Ac4Js4TN…GkTciVyXAek7oPfd…55Lx6rVv
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.

4.587 Γ— 10⁹⁢(97-digit number)
45878031588544219227…78005461091937023999
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
4.587 Γ— 10⁹⁢(97-digit number)
45878031588544219227…78005461091937023999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.587 Γ— 10⁹⁢(97-digit number)
45878031588544219227…78005461091937024001
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
9.175 Γ— 10⁹⁢(97-digit number)
91756063177088438455…56010922183874047999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.175 Γ— 10⁹⁢(97-digit number)
91756063177088438455…56010922183874048001
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
1.835 Γ— 10⁹⁷(98-digit number)
18351212635417687691…12021844367748095999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.835 Γ— 10⁹⁷(98-digit number)
18351212635417687691…12021844367748096001
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
3.670 Γ— 10⁹⁷(98-digit number)
36702425270835375382…24043688735496191999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.670 Γ— 10⁹⁷(98-digit number)
36702425270835375382…24043688735496192001
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
7.340 Γ— 10⁹⁷(98-digit number)
73404850541670750764…48087377470992383999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.340 Γ— 10⁹⁷(98-digit number)
73404850541670750764…48087377470992384001
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
1.468 Γ— 10⁹⁸(99-digit number)
14680970108334150152…96174754941984767999
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:57,787,569 XPMΒ·at block #6,817,937 Β· updates every 60s
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